A027067 a(n) = T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027052.

1, 1, 4, 10, 27, 77, 220, 632, 1821, 5257, 15206, 44068, 127951, 372173, 1084382, 3164498, 9248241, 27064057, 79296978, 232597316, 682960523, 2007206245, 5904191878, 17380855190, 51203234981, 150943862857, 445250129556