A054172 Inverse Moebius transform of A000048 (starting at term 0).

1, 2, 2, 3, 3, 6, 6, 12, 18, 32, 52, 100, 171, 322, 589, 1103, 2049, 3877, 7281, 13830, 26221, 49982, 95326, 182470, 349523, 671260, 1290573, 2485827, 4793491, 9257016, 17895680, 34637936, 67108917, 130152543, 252645143, 490857374