A071743 Expansion of (1+x^4*C)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 2, 5, 14, 43, 135, 438, 1458, 4952, 17093, 59787, 211444, 754834, 2716430, 9844071, 35892558, 131576330, 484659105, 1792926015, 6658407540, 24814260930, 92772188130, 347856470880, 1307806293924, 4928962698072