A152226 Binomial transform of A027826.

1, 2, 5, 14, 42, 132, 428, 1416, 4745, 16034, 54505, 186166, 638538, 2198692, 7598624, 26350944, 91670946, 319825796, 1118686730, 3921801820, 13775938132, 48473233032, 170815501576, 602710956464, 2128981351316, 7527515059432, 26637591204996, 94331697697688

Offset: 0

Author

Gary W. Adamson, Nov 29 2008

Keywords

• nonn

Examples

			a(3) = 14 = (1, 1, 2, 4) dot (1, 3, 3, 1) = (1 + 3 + 6 + 4).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A027826.

Programs

Maple

b:= proc(n) option remember; add(`if`(k=0, 1,
      `if`(k::odd, 0, b(k/2)))*binomial(n, k), k=0..n)
    end:
a:= n-> add(b(k)*binomial(n, k), k=0..n):
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 08 2015

Mathematica

b[n_] := b[n] = Sum[If[k == 0, 1, If[OddQ[k], 0, b[k/2]]]*Binomial[n, k], {k, 0, n}];
a[n_] := Sum[b[k]*Binomial[n, k], {k, 0, n}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jun 04 2018, from Maple *)

Formula

A007318 * A027826 as a vector. A027826 = [1, 1, 2, 4, 9, 21, 50, 120, 290,...].

Extensions

A-Number corrected by R. J. Mathar, Apr 04 2012