OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..367
R. S. Maier, Nonlinear differential equations satisfied by certain classical modular forms, arXiv:0807.1081 [math.NT], 2008-2010, p. 34 equation (7.30).
FORMULA
G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/6).
G.f.: 2F1(1/12, 7/12; 1; 1728/(1728-j)) where j is the elliptic modular invariant (A000521). - Seiichi Manyama, Jul 07 2017
a(n) ~ c * exp(2*Pi*n) / n^(7/6), where c = -Gamma(1/4)^(8/3) * Gamma(1/3)^2 / (2^(9/2) * 3^(1/6) * Pi^(7/2)) = -0.149083170913265334790743918765758886634155... - Vaclav Kotesovec, Jul 08 2017, updated Mar 05 2018
EXAMPLE
From Seiichi Manyama, Jul 08 2017: (Start)
2F1(1/12, 7/12; 1; 1728/(1728 - j))
= 1 - 84/(j - 1728) + 62244/(j - 1728)^2 - 64318800/(j - 1728)^3 + ...
= 1 - 84*q - 82656*q^2 - 64795248*q^3 - ...
+ 62244*q^2 + 122496192*q^3 + ...
- 64318800*q^3 - ...
+ ...
= 1 - 84*q - 20412*q^2 - 6617856*q^3 - ... (End)
MATHEMATICA
nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^(1/6), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 02 2017
STATUS
approved