A301549 Expansion of Product_{k>=1} (1 + x^k)^(sigma_5(k)).
1, 1, 33, 277, 1829, 12763, 89213, 584741, 3704421, 22964742, 139315315, 826585083, 4807922574, 27476514016, 154490531418, 855490577052, 4670177536402, 25157218161854, 133831334223869, 703601883107626, 3658023094714380, 18817745119097343, 95833879532504638
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..2000
Programs
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Mathematica
nmax = 30; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[5, k], {k, 1, nmax}], {x, 0, nmax}], x] -
PARI
x='x+O('x^99); Vec(prod(i=1, 99, (1+x^i)^sigma(i, 5))) \\ Altug Alkan, Mar 26 2018
Formula
a(n) ~ exp(7 * Pi^(6/7) * Zeta(7)^(1/7) * n^(6/7) / (2^(9/7) * 3^(6/7))) * (3*Zeta(7)/Pi)^(1/14) / (2^(323/504) * sqrt(7) * n^(4/7)).
G.f.: exp(Sum_{k>=1} sigma_6(k)*x^k/(k*(1 - x^(2*k)))). - Ilya Gutkovskiy, Oct 26 2018