a(n) = (n + 1)*(6*n^4 - 21*n^3 + 31*n^2 - 31*n + 30)/30.

Terms

a(0) =1a(1) =1a(2) =2a(3) =18a(4) =99a(5) =355a(6) =980a(7) =2276a(8) =4677a(9) =8773a(10) =15334a(11) =25334a(12) =39975a(13) =60711a(14) =89272a(15) =127688a(16) =178313a(17) =243849a(18) =327370a(19) =432346a(20) =562667a(21) =722667a(22) =917148a(23) =1151404a(24) =1431245a(25) =1763021a(26) =2153646a(27) =2610622a(28) =3142063a(29) =3756719