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

Terms

a(0) =2a(1) =7a(2) =42a(3) =242a(4) =1050a(5) =3537a(6) =9842a(7) =23732a(8) =51282a(9) =101675a(10) =188122a(11) =328902a(12) =548522a(13) =878997a(14) =1361250a(15) =2046632a(16) =2998562a(17) =4294287a(18) =6026762a(19) =8306650a(20) =11264442a(21) =15052697a(22) =19848402a(23) =25855452a(24) =33307250a(25) =42469427a(26) =53642682a(27) =67165742a(28) =83418442a(29) =102824925