A027291 a(n) = Sum{(k+1)*T(n,k)}, 0<=k<=[ n/2 ]+1, T given by A026009.

1, 3, 8, 16, 39, 77, 179, 354, 799, 1584, 3504, 6960, 15174, 30183, 65085, 129598, 277071, 552140, 1172348, 2337624, 4935586, 9845978, 20691318, 41292196, 86432614, 172538352, 359934704, 718680768, 1494861996, 2985378027