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A152226
Binomial transform of A027826.
1
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
0,2
LINKS
FORMULA
A007318 * A027826 as a vector. A027826 = [1, 1, 2, 4, 9, 21, 50, 120, 290,...].
EXAMPLE
a(3) = 14 = (1, 1, 2, 4) dot (1, 3, 3, 1) = (1 + 3 + 6 + 4).
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 *)
CROSSREFS
Cf. A027826.
Sequence in context: A148329 A293499 A024175 * A054393 A261589 A036768
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Nov 29 2008
EXTENSIONS
A-Number corrected by R. J. Mathar, Apr 04 2012
STATUS
approved