A289571 Coefficients in expansion of q * Product_{n>=1} (1 - q^n)^24/E_6^(3/2).

1, 732, 483336, 299831152, 179912034330, 105705360893664, 61212394149183536, 35074084087016521152, 19935701871161896669257, 11259521840932766778870360, 6326766973556024191050129528, 3540038281600931271753859693440

Offset: 1

Author

Seiichi Manyama, Jul 08 2017

Keywords

• nonn

Examples

			G.f.: q + 732*q^2 + 483336*q^3 + 299831152*q^4 + 179912034330*q^5 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..366
• M. Eichler and D. Zagier, On the zeros of the Weierstrass P-function, Math. Ann. 258 (1981/82), 399-407.

Crossrefs

Cf. A000594, A289570 (1/E_6^(3/2)).

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - x^k)^24, {k, 1, nmax}] / (1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(3/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)

Formula

Sum_{n>=1} a(n)/n^2 * exp(-2*Pi*n) = (Pi - log(5+2*sqrt(6)))/(72*sqrt(6)).

a(n) ~ c * exp(2*Pi*n) * sqrt(n), where c = sqrt(2)/(432*sqrt(Pi)) = 0.001846955001858484620092342870066582724425271440578401192897804766993... - Vaclav Kotesovec, Jul 09 2017, updated Mar 05 2018