A027243 a(n) = Sum{(k+1)*T(n,k), 0<=k<=n, T given by A026769.

1, 3, 8, 22, 55, 143, 349, 885, 2138, 5356, 12890, 32092, 77178, 191530, 460934, 1141888, 2751551, 6809421, 16431189, 40633227, 98175341, 242626935, 586867463, 1449457735, 3509084995, 8661201115, 20982916461, 51755457003