A034770 Dirichlet convolution of Bell numbers with themselves.

1, 2, 4, 11, 30, 108, 406, 1764, 8284, 42324, 231950, 1357264, 8427194, 55289280, 381798704, 2765918869, 20960284294, 165729748096, 1364153612318, 11665484452558, 103448316471556, 949739632545452, 9013431476894646