a(n) = n*(n+1)*(n+2)*(n+3)*(n^2+3*n+26)/720.

Terms

a(0) =1a(1) =6a(2) =22a(3) =63a(4) =154a(5) =336a(6) =672a(7) =1254a(8) =2211a(9) =3718a(10) =6006a(11) =9373a(12) =14196a(13) =20944a(14) =30192a(15) =42636a(16) =59109a(17) =80598a(18) =108262a(19) =143451a(20) =187726a(21) =242880a(22) =310960a(23) =394290a(24) =495495a(25) =617526a(26) =763686a(27) =937657a(28) =1143528a(29) =1385824