A071744 Expansion of (1+x^4*C)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 3, 9, 28, 91, 301, 1015, 3480, 12099, 42562, 151228, 541960, 1956734, 7110845, 25989701, 95475760, 352339875, 1305592470, 4855786680, 18120495720, 67828282410, 254606644050, 958182559854, 3614592283728, 13665501157070