A071740 Expansion of (1+x^3*C^4)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 3, 9, 29, 97, 332, 1155, 4069, 14482, 51986, 187986, 684114, 2503573, 9207590, 34013895, 126153045, 469574670, 1753616370, 6568462590, 24670834470, 92896573770, 350612243904, 1326145316766, 5026028589314, 19083966487332