A034717 Dirichlet convolution of Catalan numbers (1,2,5,14...) with themselves.

1, 4, 10, 32, 84, 284, 858, 2916, 9749, 33760, 117572, 416692, 1485800, 5350596, 19390110, 70721256, 259289580, 955298168, 3534526380, 13128309200, 48932538330, 182965362424, 686119227300, 2579809144692, 9723892804668