Number of inequivalent ways to color faces of a cube using at most n colors.

Terms

a(0) =0a(1) =1a(2) =10a(3) =57a(4) =240a(5) =800a(6) =2226a(7) =5390a(8) =11712a(9) =23355a(10) =43450a(11) =76351a(12) =127920a(13) =205842a(14) =319970a(15) =482700a(16) =709376a(17) =1018725a(18) =1433322a(19) =1980085a(20) =2690800a(21) =3602676a(22) =4758930a(23) =6209402a(24) =8011200a(25) =10229375a(26) =12937626a(27) =16219035a(28) =20166832a(29) =24885190