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A301548
Expansion of Product_{k>=1} (1 + x^k)^(sigma_4(k)).
7
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
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 23 2018
STATUS
approved