A301550 Expansion of Product_{k>=1} (1 + x^k)^(sigma_6(k)).
1, 1, 65, 795, 6971, 69317, 690756, 6316950, 55729130, 484275457, 4111328940, 34029153900, 275901508917, 2197552381491, 17207716281240, 132575879110175, 1006214596929014, 7531171360277228, 55632520744009711, 405876769498808480, 2926507055330036936
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[6, k], {k, 1, nmax}], {x, 0, nmax}], x]
Formula
a(n) ~ exp(2^(5/2) * Pi * (127*Zeta(7)/15)^(1/8) * n^(7/8)/7 - Pi * (5/(127*Zeta(7)))^(1/8) * n^(1/8) / (504 * sqrt(2) * 3^(7/8))) * (127*Zeta(7)/15)^(1/16) / (2^(9/4) * n^(9/16)).
G.f.: exp(Sum_{k>=1} sigma_7(k)*x^k/(k*(1 - x^(2*k)))). - Ilya Gutkovskiy, Oct 26 2018