a(n) = Sum_{k=0..n} k! * 2^(n-k).

Terms

a(0) =1a(1) =3a(2) =8a(3) =22a(4) =68a(5) =256a(6) =1232a(7) =7504a(8) =55328a(9) =473536a(10) =4575872a(11) =49068544a(12) =577138688a(13) =7381298176a(14) =101940887552