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

Terms

a(0) =1a(1) =3a(2) =10a(3) =39a(4) =176a(5) =903a(6) =5174a(7) =32623a(8) =223792a(9) =1655463a(10) =13110758a(11) =110510007a(12) =986490272a(13) =9287036671a(14) =91872460702a(15) =952034494431