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A152226 Binomial transform of A027826.

%I A152226 #11 Jun 04 2018 03:12:24
%S A152226 1,2,5,14,42,132,428,1416,4745,16034,54505,186166,638538,2198692,
%T A152226 7598624,26350944,91670946,319825796,1118686730,3921801820,
%U A152226 13775938132,48473233032,170815501576,602710956464,2128981351316,7527515059432,26637591204996,94331697697688
%N A152226 Binomial transform of A027826.
%H A152226 Alois P. Heinz, <a href="/A152226/b152226.txt">Table of n, a(n) for n = 0..1000</a>
%F A152226 A007318 * A027826 as a vector. A027826 = [1, 1, 2, 4, 9, 21, 50, 120, 290,...].
%e A152226 a(3) = 14 = (1, 1, 2, 4) dot (1, 3, 3, 1) = (1 + 3 + 6 + 4).
%p A152226 b:= proc(n) option remember; add(`if`(k=0, 1,
%p A152226       `if`(k::odd, 0, b(k/2)))*binomial(n, k), k=0..n)
%p A152226     end:
%p A152226 a:= n-> add(b(k)*binomial(n, k), k=0..n):
%p A152226 seq(a(n), n=0..40);  # _Alois P. Heinz_, Jul 08 2015
%t A152226 b[n_] := b[n] = Sum[If[k == 0, 1, If[OddQ[k], 0, b[k/2]]]*Binomial[n, k], {k, 0, n}];
%t A152226 a[n_] := Sum[b[k]*Binomial[n, k], {k, 0, n}];
%t A152226 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Jun 04 2018, from Maple *)
%Y A152226 Cf. A027826.
%K A152226 nonn
%O A152226 0,2
%A A152226 _Gary W. Adamson_, Nov 29 2008
%E A152226 A-Number corrected by _R. J. Mathar_, Apr 04 2012