A071726 Expansion of (1+x^3*C)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 1, 2, 6, 16, 47, 146, 471, 1562, 5291, 18226, 63648, 224808, 801686, 2882452, 10437745, 38032110, 139339635, 512996370, 1896907980, 7041759120, 26233530210, 98046684060, 367525880670, 1381386710964, 5205006015102