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A301551 Expansion of Product_{k>=1} (1 + x^k)^(sigma_7(k)). 7
1, 1, 129, 2317, 26957, 385147, 5514889, 70250881, 866874825, 10634404922, 126906497939, 1470673175003, 16705788322140, 186487470519166, 2044203433733016, 22025647881901542, 233686866722213324, 2443978994099801452, 25211475391206919299, 256716054713570158748 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ exp(9 * Pi^(8/9) * (17*Zeta(9))^(1/9) * n^(8/9) / 2^(29/9)) * (17*Zeta(9)/Pi)^(1/18) / (3 * 2^(883/1440) * n^(5/9)).

G.f.: exp(Sum_{k>=1} sigma_8(k)*x^k/(k*(1 - x^(2*k)))). - Ilya Gutkovskiy, Oct 26 2018

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[7, k], {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A013955, A107742, A301545.

Sequence in context: A036085 A000541 A023876 * A297493 A279640 A305722

Adjacent sequences:  A301548 A301549 A301550 * A301552 A301553 A301554

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 23 2018

STATUS

approved

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Last modified January 21 11:19 EST 2019. Contains 319353 sequences. (Running on oeis4.)