A047074 Sum{T(i,n-i): i=0,1,...,[ n/2 ]}, array T as in A047072.

1, 1, 1, 3, 2, 5, 6, 14, 20, 45, 70, 154, 252, 546, 924, 1980, 3432, 7293, 12870, 27170, 48620, 102102, 184756, 386308, 705432, 1469650, 2704156, 5616324, 10400600, 21544100, 40116600, 82907640, 155117520, 319929885, 601080390, 1237518450