a(n) = Sum_{k=0..2} (n+k)! * C(2,k).

Terms

a(0) =2a(1) =5a(2) =11a(3) =38a(4) =174a(5) =984a(6) =6600a(7) =51120a(8) =448560a(9) =4394880a(10) =47537280a(11) =562464000a(12) =7224940800a(13) =100111334400