A289348 Coefficients in expansion of E_6^(5/6).

1, -420, -31500, -4724160, -1314429900, -440028142344, -162555920654400, -63990327056960640, -26341675849615282380, -11210298679649742846180, -4895195936831699458605912, -2181913188022929464292248640

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)/6).

a(n) ~ c * exp(2*Pi*n) / n^(11/6), where c = -5 * 3^(1/6) * Gamma(1/4)^(40/3) / (2048*sqrt(2) * Pi^(19/2) * Gamma(1/3)^2) = -0.1571123439957640423587958439875289712533650298096956968521099309872... - 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}])^(5/6), {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), A289328 (k=5), A289293 (k=6), A289345 (k=7), A289346 (k=8), A289347 (k=9), this sequence (k=10), A289349 (k=11).

Cf. A013973 (E_6), A288851.

Sequence in context: A133712 A058834 A022046 * A107510 A023911 A135340

Adjacent sequences: A289345 A289346 A289347 * A289349 A289350 A289351

Keyword

sign

Author

Seiichi Manyama, Jul 03 2017

Status

approved