A088794 Coefficient of x^n in A(x)^(2n) is A004123(n); self-convolution is A088222.

1, 1, 1, 4, 30, 305, 3905, 59828, 1063728, 21497921, 486476766, 12184618776, 334684804952, 10005219881472, 323438539163521, 11244331792094312, 418375698771595037, 16590419690069321454, 698526596162530976512