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A294974 Coefficients in expansion of (E_2^4/E_4)^(1/8). 5
1, -42, 4032, -659904, 118064226, -22406634432, 4407587356032, -888750999070464, 182478248639753472, -37986867560948245674, 7994272624037726124672, -1697243410477799687716416, 362963150140702802158191360, -78095916585903527021840348352 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also coefficients in expansion of (E_2^8/E_8)^(1/16).

LINKS

Table of n, a(n) for n=0..13.

FORMULA

G.f.: Product_{n>=1} (1-q^n)^A294626(n).

a(n) ~ (-1)^n * 2^(13/8) * Pi * exp(Pi*sqrt(3)*n) / (Gamma(1/8) * Gamma(1/3)^(9/4) * n^(7/8)). - Vaclav Kotesovec, Jun 03 2018

MATHEMATICA

terms = 14;

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}];

(E2[x]^4/E4[x])^(1/8) + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 26 2018 *)

CROSSREFS

Cf. A004009 (E_4), A006352 (E_2), A108091, A289247, A289291, A294626, A294976.

Sequence in context: A255959 A309193 A295438 * A263057 A048538 A268546

Adjacent sequences:  A294971 A294972 A294973 * A294975 A294976 A294977

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 12 2018

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)