A119971 G.f. sum{k>=0, (x^2/(1-x)^3)^(2^k-1)}.

1, 0, 1, 3, 6, 10, 16, 30, 73, 201, 540, 1342, 3069, 6513, 12962, 24436, 44109, 77489, 136749, 256791, 550190, 1378554, 3843807, 11096833, 31607566, 86892690, 228901270, 577458936, 1397828943, 3255832291, 7318390846, 15919253376