A010756 Sum along upward diagonal of Pascal triangle from (but not including) center.

0, 0, 1, 0, 1, 3, 1, 4, 11, 5, 16, 41, 22, 63, 155, 92, 247, 591, 376, 967, 2267, 1518, 3785, 8735, 6085, 14820, 33775, 24285, 58060, 130965, 96647, 227612, 509015, 383911, 892926, 1982269, 1523117, 3505386, 7732659, 6037745, 13770404, 30208749