A027212 a(n) = Sum{(k+1)*T(n,n-k), 0<=k<=n, T given by A026725.

1, 3, 8, 23, 55, 144, 328, 816, 1808, 4358, 9485, 22377, 48097, 111720, 237917, 546161, 1154827, 2626624, 5522464, 12467540, 26092324, 58546544, 122059348, 272479782, 566242186, 1258568324, 2608232758, 5775620396, 11940756076