A301545 Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_7(k)).

1, 1, 130, 2318, 27216, 387594, 5560934, 70939556, 876220362, 10760122935, 128556693118, 1491396412267, 16958961282303, 189514843653171, 2079577812522100, 22430047600047542, 238222882236692332, 2493975995373397906, 25753455308417881148, 262500213585285366039

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1412

Formula

a(n) ~ exp(3^(17/9) * Pi^(8/9) * (Zeta(9)/5)^(1/9) * n^(8/9) / 2^(7/3) - Zeta'(-7)/2) * (Zeta(9)/(15*Pi))^(241/4320) / (3 * 2^(241/1440) * n^(2401/4320)).

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

Mathematica

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

Crossrefs

Cf. A013955, A301551.

Sequence in context: A278658 A254924 A185584 * A229329 A262108 A250212

Adjacent sequences: A301542 A301543 A301544 * A301546 A301547 A301548

Keyword

nonn

Author

Vaclav Kotesovec, Mar 23 2018

Status

approved