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A301556

Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(sigma_2(k)).

1, 2, 12, 42, 154, 498, 1640, 4990, 15092, 43840, 125220, 348478, 954294, 2561714, 6776404, 17644494, 45338734, 114971434, 288148860, 713968998, 1750662814, 4249685398, 10219662844, 24356466418, 57558783492, 134922807056, 313842321696, 724651728916

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OFFSET

0,2

COMMENTS

Convolution of A275585 and A288414.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..5000

FORMULA

a(n) ~ exp(2^(5/4) * Pi * Zeta(3)^(1/4) * n^(3/4)/3 - Pi*n^(1/4) / (3 * 2^(13/4) * Zeta(3)^(1/4)) + Zeta(3)/(8*Pi^2)) * Zeta(3)^(1/8) / (2^(15/8) * n^(5/8)).

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^DivisorSigma[2, k], {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A001157, A275585, A288414.

Sequence in context: A290928 A232584 A189491 * A055681 A296682 A351616

Adjacent sequences: A301553 A301554 A301555 * A301557 A301558 A301559

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 23 2018

STATUS

approved

URL: https://oeis.org/A301556

⇱ A301556 - OEIS