A301799 Expansion of Product_{k>=1} 1/(1 - x^k)^A000593(k).

1, 1, 2, 6, 8, 18, 34, 56, 98, 175, 290, 479, 809, 1293, 2096, 3382, 5324, 8378, 13140, 20319, 31328, 48098, 73096, 110763, 167100, 250365, 373670, 555613, 821604, 1210709, 1777718, 2598584, 3786132, 5498169, 7954764, 11473798, 16499790, 23650735, 33806012

Offset

0,3

Comments

Euler transform of A000593.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)

Formula

a(n) ~ exp((3*Pi)^(2/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(4/3) + 1/24) * Zeta(3)^(13/72) / (sqrt(A) * 2^(23/36) * 3^(49/72) * Pi^(13/72) * n^(49/72)), where A is the Glaisher-Kinkelin constant A074962.

G.f.: exp(Sum_{k>=1} sigma_2(k)*x^k/(k*(1 + x^k))). - Ilya Gutkovskiy, Oct 26 2018

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[Sum[DivisorSum[k, -(-1)^# k / # &] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)

Crossrefs

Cf. A000593, A002131, A192065, A301800.

Sequence in context: A032393 A102656 A163911 * A077638 A103015 A323859

Adjacent sequences: A301796 A301797 A301798 * A301800 A301801 A301802

Keyword

nonn

Author

Vaclav Kotesovec, Mar 26 2018

Status

approved