A096584 Antidiagonal sums of the square array A096583, in which the n-th diagonal equals the convolution of the n-th row with the antidiagonal sums (this sequence).

1, 2, 5, 12, 24, 52, 90, 186, 306, 574, 942, 1690, 2618, 4600, 7092, 11772, 18022, 29312, 43894, 69938, 103854, 161382, 238148, 363818, 530428, 799366, 1157104, 1717906, 2470426, 3623286, 5170082, 7510056, 10647032, 15305918, 21573014