A289326 Coefficients in expansion of E_6^(1/4).

1, -126, -27972, -8603784, -3156774138, -1265670056952, -536028623834760, -235629947944839168, -106414175763732002292, -49052892961209924090486, -22977990271885179647877768, -10904016663130642099838196120

Offset: 0

Author

Seiichi Manyama, Jul 02 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..367

Crossrefs

E_6^(k/12): A109817 (k=1), A289325 (k=2), this sequence (k=3), A289327 (k=4), A289328 (k=5), A289293 (k=6), A289345 (k=7), A289346 (k=8), A289347 (k=9), A289348 (k=10), A289349 (k=11).

Cf. A013973 (E_6), A288851.

Programs

Mathematica

nmax = 20; CoefficientList[Series[(1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^(1/4), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/4).

a(n) ~ c * exp(2*Pi*n) / n^(5/4), where c = -sqrt(3) * Gamma(1/4)^5 / (32 * 2^(3/4) * Pi^4) = -0.20698746071805886655919194203910626895689130674662074751291... - Vaclav Kotesovec, Jul 08 2017, updated Mar 05 2018