a(n) = Sum_{k = 0..3} (n+k)! C(3,k).

Terms

a(0) =7a(1) =16a(2) =49a(3) =212a(4) =1158a(5) =7584a(6) =57720a(7) =499680a(8) =4843440a(9) =51932160a(10) =610001280a(11) =7787404800a(12) =107336275200