A027305 a(n) = Sum{(k+1)(T(n,k)}, 0<=k<=[ (n+1)/2 ], T given by A008315.

1, 3, 5, 13, 24, 58, 111, 257, 500, 1126, 2210, 4882, 9632, 20980, 41531, 89497, 177564, 379438, 754014, 1600406, 3184016, 6720748, 13382710, 28117498, 56026984, 117254268, 233765636, 487589572, 972504704, 2022568168