Two kings and a president is pretty good, even for a White House dinner.

And last night, at a glittery state dinner that has become the trademark of the Reagan style, the king of swing played for the king of Jordan and the president of the United States.

"You may not believe this," said the president, glancing over his shoulder at the East Room portrait of George Washington as he joined Benny Goodman on stage, "but I was watching and a couple of times his foot tapped."

While the evening ended with Goodman's offer to play longer for dancing, it had begun with a classic ballroom scene. The first lady in her rhinestone-studded black chiffon had glided across the empty White House foyer with the president as the Marine Band played. "Hands Across the Sea."

"Well, we were just standing there, waiting for the king and queen, and the piano started playing, and I said this is too good to pass by, so we started dancing. It was fun," said the president.

And a few minutes later their friends from across the sea arrived from across the street. They were Jordan's King Hussein and Queen Noor, the former Lisa Halaby of Washington.

The dinner followed a day of meetings between Reagan and Hussein, who were getting to know each other. But if Mideast stability dominated the daytime discussions, by evening serious talk had been put to bed.

"I think the most important thing that was accomplished was the creation of an excellent personal relationship between the president and the king," said Richard V. Alllen, national security adviser, after dinner.

"They are both committed to peace in the Mideast, but they differ on the methods to achieve peace. The U.S. is committed to the Camp David approach, and Jordan has some objections to that . . . I don't know if they'll [settle their differences] by tomorrow afternoon, but a start has been made."

The evening had all the elements of a dazzling Hollywood opening.

The lights bounded off Mrs. Reagan's Galanos gown and Queen Noor's chunky diamond necklace as guests wearing see-throughs, sequins and slits paraded into the state rooms.

The most see-through was a St. Laurent worn by Paloma Picasso; one of the most sequined dresses was worn by Drue Claire Webster, wife of the FBI director; and the highest slit by Supreme Court Associate Justice Sandra Day O'Connor -- a black on beige polka dot pattern that was slit above the knee.

Even longtime Reagan pal Frank Sinatra came for his first state dinner under the Reagans. Sinatra, who helped arrange Goodman's performance gratis, also invited jazz drummer Buddy Rich to join the Goodman quintet.

"It's nothing official," said Sheila Tate, press secretary to Nancy Reagan, of Sinatra's impresario dealings, "but [Mrs. Reagan] hopes he'll continue. His advice is valued."

Hussein was making his first official visit to Washington since Reagan became president. While the emphasis was on getting to know each other, there was an undertone of courting Hussein as an ally in the Mideast peace negotiations.

Reagan was effusive in his praise of the Jordanian leader during after-dinner toasts, sketching an image of him as a "swashbuckling pilot" and a "man of integrity who has captured the hearts of Americans."

In his toast, Hussein spoke from the vantage point of one who has met with every American president for the last 25 years. "No visit has been more important than this one," he said, adding that the "cause of freedom and justice is very dear to us . . . there is so much at stake."

In keeping with protocol, the two leaders exchanged gifts earlier in the day. The president gave the king a sterling silver model of Hussein's private 727 jet, mounted atop a cherry wood box. The king gave Reagan a saddle of embroidered wool with multi-colored beads with leather trim, black tassels and metal stirrups.

Following dinner of poached halibut and tenderloin of beef accompanied by three wines, the 110 guests adjourned for coffee.

They were an eclectic group heavily weighted with Queen Noor's family. Her mother, who told of strolling with the king and queen's two young princes earlier in the day, said being the mother-in-law of a king "in this particular case, is wonderful."

Queen Noor's father, Najeeb Halaby, presided over a family reunion in the Green Room following Benny Goodman's performance. "My son Christian has a band in Palo Alto, and he's getting some good advice from Benny Goodman, " said Halaby.

Other guests included one of King Hussein's sons, Prince Feisal."Are you having a good time, son?" Sinatra asked as they stood in the Blue Room sipping coffee. The prince nodded.

The most enthusiastic guests were Paloma Picasso and her husband Rafael Lopez Sanchez, in Washington for the first time. They talked excitedly about lunching on the Hill, climbing to the Capitol's dome and touring the East Wing of the National Gallery, where some of her father's prints are being exhibited.

"I already knew most of the works. There was a portrait of me. I'm holding a little doll who has my face," Paloma Picasso said.

Nancy Reagan seemed to be talking to everybody even though she hasn't been feeling up to par. "She's feeling much better," said the president. "She caught a bad sore throat and laryngitis, but she's doing okay now. I didn't catch it, but I had some sinus problems when I cam back from Cancun with all that air conditioning."

The Reagans and the Jordanian royal couple sat in the front row of the East Room as Goodman and Co. launched into their first number, "Lady Be Good." Goodman moved the crowd as everyone sat tapping their toes keeping time to the beat. Later, the president and Mrs. Reagan joined Goodman on stage.

Goodman had a lot of longtime fans in the audience who recalled the big-band era. "I told him I'd been attending his concerts for years," said Justice O'Connor, who sat with him during dinner.

"I wouldn't have missed Benny Goodman for anything," saif former ambassador to Iran Richard Helms. "The entertainment's been getting better and better here since the Reagans."

For the host, who was "lucky enough to grow up in the big big-band era," it was musical royalty entertaining visiting royalty, royally. "Be kind to the rest of those here who are too young to know the big-band era. They'll never know what they missed," said Reagan.

At evening's end, he and the first lady escorted their guests of honor into the warm night air on the North Portico, then did a couple of turns to the Marine Band back in the foyer where their evening began. Dinner Guest List

The following is a guest list of last night's White House state dinner for King Hussein and Queen Noor of Jordan :

The President and Mrs. Reagan

King Hussein and Queen Noor

Mudar Badran, prime minister and minister of defense

Ahmad Lawzi, chief of royal court

Amer Khammash, minister of court

Sharif Zald Bin Shaker, commander-in-chief of Jordon's armed forces, and Mrs. Bin Shaker

Mrs. Leila Sharaf, wife of the former prime minister

Adnan Abu-Oudeh, minister of Information

Marwan Qasim, minister of foreign affairs

Ambassador Matall of Jordan and Mrs. Matall

Yanal Hikmat, chief of royal protocol

Samir Farral, King Hussein's personal physician

Prince Feisal, son of King Hussien

Faud Ayoub, press director, royal palace

The Rev. and Mrs. Ralph D. Abernathy, Atlanta, Ga.

Richard V. Allen, assistant to the president for national security affairs, and Mrs. Allen

Robert Anderson, chairman, Rockwell International Corp., Pittsburgh, Pa., and Mrs. Anderson

Leonore Annenberg, chief of protocol, and Walter H. Annenberg

James A. Baker Ill, chief of staff, and assistant to the president, and Mrs. Baker

Frank R. Barnett, National Strategy Information Center, New York City, and Mrs. Barnett

Gen. Robert H. Barrow, Commandent of the Marine Corps., and Mrs. Barrow

Terrel Bell, secretary of education, and Mrs. Bell

L. Dean Brown, president, Middle East Institute, Washington, and Mrs. Brown

James L. Buckley, under secretary of state for coordination of security assistance programs, and Mrs. Buckley

Vice President George Bush and Mrs. Bush

Dr. W. Glenn Campbell, director, Hoover Institute, Stanford University, and Mrs. Campbell

William J. Casey, director, Central Intelligence Agency, and Mrs. Casey

Michael K. Deaver, deputy chief of staff and assistant to the president, and Mrs. Deaver

James Charles Evers, Fayette, Miss.

John Gannon, president, International Association of Fire Fighters, and Mrs. Gannon

Richard L. Gelb, chairman, Bristol-Myers Co. New York City, and Mrs. Gelb

Benny Goodman, musician, New York City

Alexander Haig, secretary of state, and Mrs. Haig

Alexa Halaby, sister of Queen Noor, Dallas, Tex.

Christian Halaby, brother of Queen Noor, and Mrs. Halaby, Atherton, Calif.

Doris, C. Halaby, mother of Queen Noor, New York City

Naleeb Halaby, father of the queen, Washington and Mrs. Halaby

Prentis Cobb Hale, chairman, executive committee, Carter Hawley Hale Stores, Inc., San Francisco, and Mrs. Hale

Mr. and Mrs. Paul Harvey, River Forest, Ill.

The Rev. Theodore M. Hesburgh, president, University of Notre Dame

Joseph J. Jacobs, chairman, Jacobs Engineering Group, Pasadena, Calif., and Mrs. Jacobs

Rep. Trent Lott (R-Miss.) and Mrs. Lott

William B. Macomber, president, Metropolitan Musuem of Art, New York City, and Mrs. Macomber

W. Robert McLellan, vice president, FMC Corp., Chicago, and Mrs McLellan

Edwin Meese, Ill, counselor to the president, and Mrs. Meese

Mrs. Thomas M. Mayer, London

Rep. Robert H. Michel (R-Ill.) and Mrs. Michel

Jeremiah Milbank, New York City, and Mrs. Milbank

Sandra D. O'Connor, Supreme Court justice and John H. O'Connor III

Paloma Picasso and Rafael Lopez Sanchez, New York City

Samuel R. Pierce, secretary of housing and urban development and Mrs. Pierce

Richard M. Richards, chairman, Republican National Committee, and Mrs. Richards

Mr. and Mrs. Joe Rodgers, Nashville, Tenn.

William P. Rogers, Rogers & Wells, Washington and New York City, and Mrs. Rogers

Mr. and Mrs. Archibald B. Roosevelt Jr., Washington

Elton H. Rule, president and chief executive officer, American Broadcasting Companies Inc., New York City, and Mrs. Rule

Mr. and Mrs. George Scharffenberger, Rolling Hills, Calif.

Mr. and Mrs. Frank Sinatra, Hollywood, Calif.

Sen. Ted Stevens (R-Alaska) and Mrs. Stevens

Helen Thomas, United Press International

Nicholas A. Veliotes, assistant secretary of state for Near Eastern and South Asian affairs, and Mrs. Veliotes

Richard N. Viets, American ambassador to Jordan, and Mrs. Viets

William H. Webster, director, Federal Bureau of Investigation, and Mrs. Webster

Rep. Clement J. Zablocki (D-Wis.)