a(n) = (n + 4)*(n + 3)*(n + 2)*(n + 1)*n / 5 = 24*A000389(n+4).

Terms

a(0) =0a(1) =24a(2) =144a(3) =504a(4) =1344a(5) =3024a(6) =6048a(7) =11088a(8) =19008a(9) =30888a(10) =48048a(11) =72072a(12) =104832a(13) =148512a(14) =205632a(15) =279072a(16) =372096a(17) =488376a(18) =632016a(19) =807576a(20) =1020096a(21) =1275120a(22) =1578720a(23) =1937520a(24) =2358720a(25) =2850120a(26) =3420144a(27) =4077864a(28) =4833024a(29) =5696064