Running -- the Olympian sort, not the campaign kind -- was one of the first things President Jimmy Carter wanted to talk over with President Daniel arap Moi of Kenya.

"As a famous runner myself when the land is flat, I have always admired the achievements of Kenya's world record holders . . .They run up and down hills with no difficulty at all," said President Carter to a roomful of sympathetic laughter at the White House last night. He quickly went on to thank the Kenyans for their support of a boycott of the Moscow Summer Olympics: "Such action of leadership is typical of the principles that have permeated the life of our guest."

Though President Moi, the quiet, former schoolteacher, did not speak of his own athletic prowess, he too alluded to his country's reputation for fast running. "We made sacrifices, because we were very hopeful we were going to win a gold medal. Others, of course, are participating with no hopes of winning one," he said during his 25-minute toast at last night's state dinner in his honor.

Though President Moi is the fourth African leader to visit the United States during the Carter adminstration, the Kenyan leader received the first full-fledged state treatment. In fact, pomp and ceremony seem to have returned to the Carter White House. At yesterday morning's arrival ceremony on the South Lawn, "Hail to the Chief" supplanted "Man of the Hour." And the military men were back too, holding the 56 flags of the states and territories. The White House, according to a spokesman, reintroduced the ceremonial trappings in stages, starting with the recent visit of British Prime Minister Margaret Thatcher.

Also, the custom of inviting to the Carter White House large contingents of citizens with ethnic and historic ties to the guest of honor was followed last night. Among the 70-odd guests were Thurgood Marshall, the associate Supreme Court justice who helped shape Kenya's constitution; Patricia Roberts Harris, the secretary of Health, Education and Welfare; Clifford Alexander, secretary of the Army, who said mail on the draft registration was "running the gamut"; Eleanor Holmes Norton, the chair of the Equal Employment Opportunity Commission; Joyce Ladner Carrington, sociologist and author; Benjamin Hooks, executive director of the NAACP; historian John Hope Franklin; and Jesse Hill, Atlanta businessman and Carter confidante.

Most of the guests quickly vowed allegiance to the Carter-Mondale reelection drive. "This is the first president who has made African policy a reality," said Clarence Avant, a Los Angeles entertainment businessman. Washington Mayor Marion Barry, an announced Carter supporter, said he was "in and out of the White House. Maybe someday we will be living here." George Weaver, an assistant secretary during John Kennedy's adminstration, offered that it was "too early to campaign" for either Kennedy or Carter.

Kenneth Gibson, the mayor of Newark, N.J., took his admiration of the president to the level of imitation earlier this week by asking for the resignation of 500 of his city officials. "Yes, I was thinking of President Carter's move last summer," he said. "It created some kind of stir, but with all the criticism it came out quite well. We are going through a similar reevaluation."

In neither President Carter's nor President Moi's remarks was there a mention of Kenya's recent offer of military facilities along its Indian Ocean coast to the United States. But this agreement was primarily credited by the foreign specialists for the growing status of Kenya's close ties to the United States. "Kenya is one of the great success stories of economic and political development in East Africa. They seem ready to offer the use of their facilities," said Assistant Secretary of State for African Affairs Richard Moose.

The growing importance of Kenya in American's Persian Gulf policy was viewed skeptically by Randall Robinson, the executive director of a lobbying group, TransAfrica. "We oppose the base policy with Kenya because we didn't want to bring the cold war to Africa, but the Kenyans have insisted that the United States will not be opening a base." Calling Kenya "a moderating force" in the East African region, Rep. Stephen Solarz (D-N.Y.), the chairman of the House subcommittee on Africa, said, "I'm anxious to get President Moi's reaction to our request for a base in Berbera [in Somalia] because of the traditional hostility between those two countries."

When the two presidents entered the State Dining Room, the evenrable pianist Eubie Blake refused to stand, telling his dinner companion. "I'm too tired." But when it came time for the 96-year-old Blake to surprise the guests and join the evening's scheduled performers, Wilfred Delphin and Edwin Romain, he was in typical form. "A ragtime," Blake told the audience, introducing one number, "half the tempo I used to play." Addressing President Moi, Blake said he had never been to Africa though he hoped to go "in the next 15 to 20 years."

Noticeably absent from the gestivities was one of Carter's latest globetrotting emissaries, Muhammad Ali. His recent trip to Africa to enlist support for the Olympics boycott stirred up considerable controversy and Ali was snubbed by one of the adminstration's allies, President Julius Nyerere of Tanzanai, but was received by President Moi. He had been invited, said White House social secretary Gretchen Posten but sent his regrets "because he would be out of the country."

Barbara Watson, the undersecretary of State for Counsular Affairs, said she had no idea where Ali was; "I can't keep up with the secretary [Cyrus Vance], much less Ali."

The following were President and Mrs. Carter's guests at last night's state dinner for President Moi: Charles Njonio, attorney general. Robert J. Ouko, minister of foreign affairs. Godrey G. Kariuki, minister of state, Office of the President. Nicholas K. Biwott, minister of state, Office of the President. Zacharia T. Onyonka, minister of economic planning and development. Jeremiah G. Kiereini, premanent secretary, Office of the President. John P. Mbogua, ambassador of Kenya; & Mrs. Mbogua. Philip Ndegwa, economic adviser, Office of the President. Simon Nyachae, permanent secretary, Office of the President. Harris M. Mule, permanent secretary, Ministry of Economic Planning and Development. Leo F. Odero, chief of protocol. Charles Maina, ambassador of Kenya to the United Nations. Andrew L. Ngeny, private secretary/comptroller, State House. Dr. Antonia F. Bagshaw, president's physician, State House. John Githuku, deputy permanent secretary to the Vice President's Office. Thurgood Marshall, associate justice of the Supreme Court; & Mrs. Marshall. Harold Brown, secretary of defense; & Mrs. Brown. Patricia Roberts Harris Secretary of Health, education & welfare; & Judge William B. Harris. Zbigniew Brzezinski, assistant to the president for national security affairs; & Mrs. Brzezinski. Sen. Jim Sasser (D-Tenn.); & Mrs. Sasser. Sen. Nancy L. Kassebaum (D-Kan.). Sen. J. James Exon (D-Neb.); & Mrs. Exon. Warren Christopher, deputy secretary of state; & Mrs. Christopher. Rep. Parren J. Mitchell (D-Md.).

Rep. Charles B. Rangel (D-N.Y.); & Mrs. Rangel. Rep. Don Bonker (D-Wash.); & Mrs. Bonker. Rep. Stephen J. Solarz (D-N.Y.); & Mrs. Solarz. Lloyd N. Cutler, counsel to the president; & Mrs. Cutler. Clifford L. Alexander Jr., secretary of the army; & Mrs. Alexander. Sam W. Brown Jr., dir., ACTION. Wilbert J. LeMelle, American ambassador to Kenya. Abelardo Valdez, chief of protocol; & Mrs. Valdex. Louis E. Martin, special assistant to the president; & Mrs. Martin. Richard M. Moose, assistant secretary of state for African affairs; & Mrs. Moose. Gerald Funk, National Security Council; & Mrs. Funk. John G. Heimann, comptroller of the currency; & guest Susan Wagner. Marion Barry, mayor of the District of Columbia; & Mrs. Barry. Mrs. Robinson McIlvanine; & Guest Stevenson McIlvaine. Thomas Ehrilich, dir., U.S. International Development Cooperation Agency; & Mrs. Ehrlich. Michael Pertschuk, chmn., Federal Trade Commission; & Mrs. Pertschuk. Eleanor Holmes Norton, chair, Equal Employment Opportunity Commission; & Mr. Norton. Arrington Dixon, chmn. District of Columbia Council; guest Mrs. Charlene Drew Jarvis. William C. Harrop, deputy assistant secretary of state; and Mrs. Harrop. Maj. Gen. Kenneth Joe Hodson, USA, Ret.; and Mrs. Hodson. Daniel Malachulk, deputy special assistant, White Hosue; and Mrs. Malachuk. John C. Anderson, Philadephia City Council. Clarence Avant, pres., Tabu Recording Co., Beverly Hills, Calif.; and Mrs. Avant. Mr. and Mrs. Eubie Blake, Brooklyn, N.Y. Roland W. Burris, comptroller, State of Illinois; and Mrs. Burris. Mr. and Mrs. Clarence Cade, Cincinnati, Ohio. J. J. Cafaro, exec. vice pres., Cafaro Co., Youngstown, Ohio; and Mrs. Cafaro. Mr. and Mrs. Walter Carrington, New York City. Peggy Cooper, chmn., District of Columbia Arts Council; and Conrad Cafritz. Mr. and Mrs. David Cunningham, Los Angeles, Calif. Wilfred Delphin; and guest Mr. Allan Lokos. George Fan; and guest Daisy Chen. Mr. and Mrs. Arthur Feinberg, Wauregan, Conn. William Fitzgerald pres., Independence Federal Savings & Loan Association of Washington; and Mrs. Fitzgerald. John Hope Franklin, University of Chicago; and Mrs. Franklin. Kenneth Gibson, mayor of Newark, N.J.; and Mrs. Gibson. Mr. and Mrs. John W. Hechinger, Washington, D.C. Charles Henry, Panama City Beach, Fla.; and guest Heather Taylor. Jesse Hill Jr., pres. Atlanta Life Insurance Co., Altanta, Ga.; and guest Ariza Hill. Benjamin L. Hooks, exec. dir., NAACP, New York City; and Mrs. Hooks. C. Payne Lucas, exec. dir., AFRICARE, D.C.; & Mrs. Lucas. Mr. & Mrs. Sabin Robbins IV, Washington, D.C. Dr. Warren Robbins, dir., Museum of African Art Smithsonian Institution; & (guest Evelyn Sessler). Randall Robinson, exec. dir., Trans-Africa, Washington, D.C.; & mrs. Robinson. Edwin Romain & guest Naomi Rhodes. Dr. William Rutherford & Waldi Naimie, Washington, D.C. Arnold A. Saltzman, chmn., The Seagrave Corp., New York City; Mrs. Saltzman. Mr. & Mrs. Thomas H. Tipton, Minneapolis, Minn. Mr. & Mrs. William L. Tucker, Philadelphia, Pa. Mr. & Mrs. George L. P. Weaver, Washington, D.C. Wayne Wells, vice pres. & Treas., General Dynamics, St. Louis, Mo.; & Mrs. Wells. Lee Williams, Vice pres., American Retail Federation, D.C. ; & Mrs. Williams. Rev. Claude S. Wyatt; & Addie Wyatt, vice pres., United Food & Commercial workers Union.