a(n) = (n+1)(n+2)^2*(n+3)(2n+3)(5n^2 + 19n + 20)/720.

Terms

a(0) =1a(1) =22a(2) =182a(3) =915a(4) =3388a(5) =10192a(6) =26376a(7) =60894a(8) =128535a(9) =252406a(10) =467038a(11) =822185a(12) =1387386a(13) =2257360a(14) =3558304a(15) =5455164a(16) =8159949a(17) =11941158a(18) =17134390a(19) =24154207a(20) =33507320a(21) =45807168a(22) =61789960a(23) =82332250a(24) =108470115a(25) =141420006a(26) =182601342