A047131 Sum{T(i,n-i): i=0,1,...,n}, array T as in A047131.

1, 2, 3, 6, 10, 20, 35, 70, 140, 252, 504, 932, 1864, 3493, 6986, 13972, 26265, 52530, 100168, 200336, 384573, 769146, 1538292, 2950530, 5901060, 11422700, 22845400, 44403564, 88807128, 177614256, 344644881, 689289762, 1346117062