A026965 a(n) = Sum{(k+1)*T(n,k)}, 0<=k<=n, T given by A026626.

1, 3, 10, 25, 66, 154, 360, 810, 1810, 3982, 8700, 18850, 40614, 87030, 185680, 394570, 835578, 1763998, 3713700, 7798770, 16340302, 34166086, 71303160, 148548250, 308980386, 641728494, 1330992460, 2757055810, 5704253430