A289328 Coefficients in expansion of E_6^(5/12).

1, -210, -37800, -10300080, -3534651750, -1351633962672, -551776752641520, -235367241169341120, -103623939263346377400, -46723958347194591810690, -21464711387762586693907248, -10009787904868201520473221840

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

G.f.: Product_{n>=1} (1-q^n)^(5*A288851(n)/12).

a(n) ~ c * exp(2*Pi*n) / n^(17/12), where c = -5 * Gamma(1/12) * Gamma(1/4)^(20/3) / (128 * 2^(11/12) * 3^(2/3) * Pi^5 * Gamma(1/3)^2) = -0.2792181117471536554156263079143941137076647484619917046386429000631... - Vaclav Kotesovec, Jul 08 2017, updated Mar 05 2018

Mathematica

nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^(5/12), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Crossrefs

E_6^(k/12): A109817 (k=1), A289325 (k=2), A289326 (k=3), A289327 (k=4), this sequence (k=5), A289293 (k=6).

Cf. A013973 (E_6), A288851.

Sequence in context: A187308 A229754 A089514 * A014979 A356690 A362945

Adjacent sequences: A289325 A289326 A289327 * A289329 A289330 A289331

Keyword

sign

Author

Seiichi Manyama, Jul 02 2017

Status

approved