a(n) = n*(n + 1)*(n + 2)*(n^2 - n + 4)/24.

Terms

a(0) =1a(1) =6a(2) =25a(3) =80a(4) =210a(5) =476a(6) =966a(7) =1800a(8) =3135a(9) =5170a(10) =8151a(11) =12376a(12) =18200a(13) =26040a(14) =36380a(15) =49776a(16) =66861a(17) =88350a(18) =115045a(19) =147840a(20) =187726a(21) =235796a(22) =293250a(23) =361400a(24) =441675a(25) =535626a(26) =644931a(27) =771400a(28) =916980a(29) =1083760