A034740 Dirichlet convolution of b_n=2^(n-1) with Bell numbers.

1, 3, 6, 15, 31, 92, 267, 1023, 4404, 21705, 116999, 680790, 4217693, 27653099, 190915798, 1382993235, 10480207683, 82865009684, 682077068303, 5832742772351, 51724159284888, 474869818486877, 4506715742641627