G.f.: 2C(x)/(3-sqrt(1-4xC(x))) where C = g.f. for A000108.

Terms

a(0) =1a(1) =0a(2) =0a(3) =-1a(4) =-6a(5) =-30a(6) =-142a(7) =-660a(8) =-3054a(9) =-14154a(10) =-65886a(11) =-308442a(12) =-1452940a(13) =-6887508a(14) =-32852082a(15) =-157630609a(16) =-760599954a(17) =-3689418510a(18) =-17984138984a(19) =-88063955880a(20) =-433048404780