OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..425
R. S. Maier, Nonlinear differential equations satisfied by certain classical modular forms, arXiv:0807.1081 [math.NT], 2008-2010, p. 34 equation (7.29b).
FORMULA
G.f.: Product_{n>=1} (1-q^n)^(A110163(n)/2).
a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(3/2), where c = 3*Gamma(1/3)^9 / (32*sqrt(2)*Pi^(13/2)) = 0.27646925986847687648926173728588572192308632719... - Vaclav Kotesovec, Jul 02 2017, updated Mar 05 2018
G.f.: 3F2(1/6, 1/2, 5/6; 1, 1; 1728/j) where j is the elliptic modular invariant (A000521). - Seiichi Manyama, Jul 07 2017
MATHEMATICA
terms = 14;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E4[x]^(1/2) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 23 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 02 2017
STATUS
approved