A010757 Sum along upward diagonal of Pascal triangle from center.

1, 0, 1, 2, 1, 3, 7, 4, 11, 25, 16, 41, 92, 63, 155, 344, 247, 591, 1300, 967, 2267, 4950, 3785, 8735, 18955, 14820, 33775, 72905, 58060, 130965, 281403, 227612, 509015, 1089343, 892926, 1982269, 4227273, 3505386, 7732659, 16438345, 13770404