a(n) = Sum_{k=1..n} k^(n-k)*binomial(n-1,k-1).

Terms

a(0) =1a(1) =2a(2) =6a(3) =23a(4) =104a(5) =537a(6) =3100a(7) =19693a(8) =136064a(9) =1013345a(10) =8076644a(11) =68486013a(12) =614797936a(13) =5818490641a(14) =57846681092a(15) =602259154853