A261584 Expansion of Product_{k>=1} (1 + 2*x^k)/(1 - 2*x^k).

1, 4, 12, 36, 92, 228, 540, 1236, 2748, 6004, 12876, 27252, 57036, 118308, 243564, 498564, 1015484, 2060484, 4167804, 8409588, 16934748, 34049940, 68378220, 137185428, 275026476, 551052676, 1103618508, 2209525092, 4422484764, 8850120420, 17707920924

Offset: 0

Author

Vaclav Kotesovec, Aug 25 2015

Keywords

• nonn

Crossrefs

Cf. A032302, A070933, A261563.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 40; CoefficientList[Series[Exp[Sum[2^(2*k)/(2*k-1)*x^(2*k-1)/(1 - x^(2*k-1)), {k, 1, nmax}]], {x, 0, nmax}], x]
(O[x]^30 - QPochhammer[-2, x]/(3 QPochhammer[2, x]))[[3]] (* Vladimir Reshetnikov, Nov 20 2015 *)

Formula

a(n) = c * 2^n, where c = 1/(A048651 * A083864) = 2*Product_{j>=1} (2^j+1)/(2^j-1) = 16.5119758715565001310882816988645462530540032335764606912075051272567456...