A010753 Sum along upward diagonal of Pascal triangle up to (but not including) center.

0, 1, 1, 1, 4, 5, 6, 17, 23, 30, 73, 103, 141, 314, 455, 643, 1350, 1993, 2881, 5798, 8679, 12761, 24872, 37633, 56070, 106573, 162643, 244906, 456169, 701075, 1064866, 1950697, 3015563, 4613544, 8334539, 12948083, 19930544, 35582783, 55513327