A049168 Recip transform of 2*(1 + x^3 + x^5 + x^6)-1/(1-x).

1, 1, 3, 9, 33, 125, 501, 2065, 8739, 37687, 165133, 732915, 3288431, 14890715, 67964547, 312347427, 1444163637, 6712965621, 31352965503, 147060094981, 692437504773, 3271741774097, 15507950956329, 73720541568021