a(n) = Sum_{i=0..n} 3^i*i!.

Terms

a(0) =1a(1) =4a(2) =22a(3) =184a(4) =2128a(5) =31288a(6) =556168a(7) =11578648a(8) =276118168a(9) =7418685208a(10) =221695696408