a(n) = (n-1)*n*(n+1)*(n+2)*(2n+11)/120.

Terms

a(0) =0a(1) =3a(2) =17a(3) =57a(4) =147a(5) =322a(6) =630a(7) =1134a(8) =1914a(9) =3069a(10) =4719a(11) =7007a(12) =10101a(13) =14196a(14) =19516a(15) =26316a(16) =34884a(17) =45543a(18) =58653a(19) =74613a(20) =93863a(21) =116886a(22) =144210a(23) =176410a(24) =214110a(25) =257985a(26) =308763a(27) =367227a(28) =434217a(29) =510632