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

Terms

a(0) =1a(1) =2a(2) =6a(3) =18a(4) =58a(5) =202a(6) =762a(7) =3114a(8) =13754a(9) =65386a(10) =332922a(11) =1806506a(12) =10398266a(13) =63226858a(14) =404640250a(15) =2716838186a(16) =19083233210a(17) =139874994282