A027236 a(n) = Sum{(k+1)*T(n,n-k), 0<=k<=n, T given by A026758.

1, 3, 8, 23, 55, 149, 339, 889, 1966, 5059, 10985, 27939, 59898, 151210, 321155, 806806, 1701347, 4260511, 8933737, 22325426, 46600476, 116300505, 241846731, 603086027, 1250175771, 3116094702, 6442311137, 16054097455, 33114584924