a(n) = (n+1)*(n+2)*(n+3)*(19*n^3 + 111*n^2 + 200*n + 120)/720.

Terms

a(0) =1a(1) =15a(2) =93a(3) =372a(4) =1141a(5) =2926a(6) =6594a(7) =13476a(8) =25509a(9) =45397a(10) =76791a(11) =124488a(12) =194649a(13) =295036a(14) =435268a(15) =627096a(16) =884697a(17) =1224987a(18) =1667953a(19) =2237004a(20) =2959341a(21) =3866346a(22) =4993990a(23) =6383260a(24) =8080605a(25) =10138401a(26) =12615435a(27) =15577408a(28) =19097457a(29) =23256696