A289327 Coefficients in expansion of E_6^(1/3).

1, -168, -33768, -9806496, -3482370024, -1364023149552, -567278132268960, -245678241438057792, -109559333350138970088, -49951945835561166375048, -23173552482577051154061168, -10901813191731667585777068000

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), A289326 (k=3), this sequence (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}])^(1/3), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(A288851(n)/3).

a(n) ~ c * exp(2*Pi*n) / n^(4/3), where c = -3^(1/6) * Gamma(1/4)^(16/3) * Gamma(1/3) / (32 * 2^(1/3) * Pi^5) = -0.25096087408563316781920388861983614789... - Vaclav Kotesovec, Jul 08 2017, updated Mar 05 2018