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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..367
Programs
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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 *)
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