A301552 Expansion of Product_{k>=1} (1 + x^k)^(sigma_8(k)).

1, 1, 257, 6819, 105251, 2175749, 44995096, 796670938, 13805853214, 240569119333, 4044892975196, 65784204818948, 1051532586300939, 16521916387136217, 254423642953508270, 3848289482388789293, 57317953928614093036, 841172595390506945766, 12168324212099663732171

Offset

0,3

Links

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

Formula

a(n) ~ exp(5 * 2^(4/5) * Pi * (511*Zeta(9)/33)^(1/10) * n^(9/10)/9 + Pi * (11/(511*Zeta(9)))^(1/10) * n^(1/10) / (480 * 2^(4/5) * 3^(9/10))) * (511*Zeta(9)/33)^(1/20) / (2^(11/10) * sqrt(5) * n^(11/20)).

G.f.: exp(Sum_{k>=1} sigma_9(k)*x^k/(k*(1 - x^(2*k)))). - Ilya Gutkovskiy, Oct 26 2018

Mathematica

nmax = 30; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[8, k], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A013956, A107742, A301546.

Sequence in context: A036086 A000542 A023877 * A279641 A168116 A086022

Adjacent sequences: A301549 A301550 A301551 * A301553 A301554 A301555

Keyword

nonn

Author

Vaclav Kotesovec, Mar 23 2018

Status

approved