A034750 Dirichlet convolution of Fibonacci numbers with Bell numbers.

1, 2, 4, 9, 20, 64, 216, 906, 4178, 21222, 116064, 678790, 4213830, 27645030, 190899972, 1382960445, 10480143744, 82864876682, 682076810340, 5832742233094, 51724158246750, 474869816290526, 4506715738475980