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

Terms

a(0) =1a(1) =1a(2) =3a(3) =11a(4) =51a(5) =287a(6) =1899a(7) =14447a(8) =124251a(9) =1192127a(10) =12623979a(11) =146250287a(12) =1840024251a(13) =24983863967a(14) =364140992139