A299712 Coefficients in expansion of (E_14/E_2^14)^(1/4).

1, 78, -44928, -14386944, -5323508814, -1996794824544, -833028042023424, -358702721913389568, -160514702770156497360, -73334654476723097306706, -34151846554093744054455552, -16125009656471947012310740224

Offset

0,2

Links

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

Formula

a(n) ~ -2^(3/4) * sqrt(3) * Pi^(11/2) * exp(2*Pi*n) / (864 * Gamma(3/4)^9 * n^(5/4)). - Vaclav Kotesovec, Jun 03 2018

Mathematica

terms = 12;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E10[x_] = 1 - 264*Sum[k^9*x^k/(1 - x^k), {k, 1, terms}];
E14[x_] = E4[x]*E10[x];
(E14[x]/E2[x]^14)^(1/4) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Crossrefs

Cf. A294976, A294978, A295788, A299713.

Sequence in context: A119216 A119236 A126998 * A159402 A093239 A299713

Adjacent sequences: A299709 A299710 A299711 * A299713 A299714 A299715

Keyword

sign

Author

Seiichi Manyama, Feb 17 2018

Status

approved