A035530 Binomial transform of A003603.
1, 2, 4, 9, 20, 44, 97, 212, 455, 961, 2014, 4219, 8863, 18662, 39298, 82584, 173008, 361321, 752823, 1566271, 3256418, 6768409, 14064705, 29213846, 60634364, 125706899, 260227836, 537737396, 1108954613
Offset: 0