A301548 Expansion of Product_{k>=1} (1 + x^k)^(sigma_4(k)).

1, 1, 17, 99, 491, 2429, 12056, 56618, 259074, 1155193, 5044288, 21585280, 90694483, 374661505, 1524090522, 6111565745, 24181962002, 94491963120, 364920615165, 1393789672170, 5268145436728, 19715988877445, 73096492576283, 268589397735778, 978533798885874

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..3000

Formula

a(n) ~ exp(6^(2/3) * Pi * (31*Zeta(5)/7)^(1/6) * n^(5/6)/5 + Pi *(7/(31*Zeta(5)))^(1/6) * n^(1/6) / (240*6^(2/3))) * (31*Zeta(5)/7)^(1/12) / (2^(7/6) * 3^(2/3) * n^(7/12)).

G.f.: exp(Sum_{k>=1} sigma_5(k)*x^k/(k*(1 - x^(2*k)))). - Ilya Gutkovskiy, Oct 26 2018

Mathematica

nmax = 40; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[4, k], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A001159, A107742, A301542.

Sequence in context: A265838 A098997 A257449 * A337166 A139497 A139913

Adjacent sequences: A301545 A301546 A301547 * A301549 A301550 A301551

Keyword

nonn

Author

Vaclav Kotesovec, Mar 23 2018

Status

approved