a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(4*n^2+15*n+15)/720.

Terms

a(0) =1a(1) =17a(2) =122a(3) =560a(4) =1946a(5) =5586a(6) =13944a(7) =31284a(8) =64515a(9) =124267a(10) =226226a(11) =392756a(12) =654836a(13) =1054340a(14) =1646688a(15) =2503896a(16) =3718053a(17) =5405253a(18) =7710010a(19) =10810184a(20) =14922446a(21) =20308310a(22) =27280760a(23) =36211500a(24) =47538855a(25) =61776351a(26) =79522002a(27) =101468332a(28) =128413160a(29) =161271176