A034768 Dirichlet convolution of Catalan numbers with themselves.

1, 2, 4, 11, 28, 88, 264, 868, 2864, 9752, 33592, 117676, 416024, 1486064, 5348936, 19390573, 70715340, 259292608, 955277400, 3534536244, 13128241368, 48932567632, 182965127280, 686119347008, 2579808294844, 9723893218928