A027298 a(n) = Sum_{k=0..m} (k+1) * A026022(n, k), where m=n for n=0,1 and m = floor((n+3)/2) for n >= 2.

1, 3, 8, 20, 43, 101, 208, 472, 958, 2126, 4288, 9368, 18835, 40673, 81632, 174704, 350266, 744290, 1491232, 3150424, 6309246, 13265138, 26557408, 55610960, 111311068, 232279836, 464856832, 967155824, 1935314563