A289347 Coefficients in expansion of E_6^(3/4).

1, -378, -36288, -6664896, -1950813774, -672039262944, -253536117254784, -101485291597998336, -42360328701954544176, -18242860786892766495450, -8049299329628263783504512, -3621056234759774113947852096

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1-q^n)^(3*A288851(n)/4).

a(n) ~ c * exp(2*Pi*n) / n^(7/4), where c = -3^(5/2) * Gamma(1/4)^11 / (2048 * 2^(3/4) * Pi^9) = -0.21604472104032272720247495618663130188448925463945370445... - 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}])^(3/4), {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), this sequence (k=9), A289348 (k=10), A289349 (k=11).

Cf. A013973 (E_6), A288851.

Sequence in context: A248915 A225839 A221803 * A171115 A328552 A225994

Adjacent sequences: A289344 A289345 A289346 * A289348 A289349 A289350

Keyword

sign

Author

Seiichi Manyama, Jul 03 2017

Status

approved