a(n) = n!*LaguerreL(n, -3).

Terms

a(0) =1a(1) =4a(2) =23a(3) =168a(4) =1473a(5) =14988a(6) =173007a(7) =2228544a(8) =31636449a(9) =490102164a(10) =8219695239a(11) =148262469336