a(n) = n!*[x^n] sinh(x/(1 - x))/(1 - x).

Terms

a(0) =0a(1) =1a(2) =4a(3) =19a(4) =112a(5) =801a(6) =6756a(7) =65563a(8) =717760a(9) =8729857a(10) =116570980a(11) =1693096131a(12) =26548383984a(13) =446689827169