A107269 Diagonal sums of A107267, viewed as a number triangle.
1, 0, 1, 1, 3, 6, 16, 44, 136, 457, 1669, 6547, 27334, 120465, 557094, 2692528, 13564940, 71102869, 387132791, 2185813423, 12775466408, 77154694819, 480630407368, 3083443893896, 20344187534051, 137884769704754
Offset: 0
Formula
a(n)=sum{k=0..n, sum{j=0..n-2k, (1/(j+1))C(j+1, n-2k-j+1)C(n-2k, j)k^j}}