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

Terms

a(0) =1a(1) =1a(2) =6a(3) =47a(4) =490a(5) =6417a(6) =101178a(7) =1866139a(8) =39425322a(9) =938856053a(10) =24883226698a(11) =726510389607