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A294183 Coefficients in expansion of E_6/E_8. 3
1, -984, 393768, -129252576, 38684099112, -10970838627984, 3003345011096352, -801909012374388672, 210169391033048138280, -54295810529811041175672, 13867098270790394508774768, -3508693915623201191415922848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..421

FORMULA

Convolution inverse of A288840.

a(n) ~ (-1)^n * 512 * Pi^12 * exp(Pi*sqrt(3)*n) * n / (3 * Gamma(1/3)^18). - Vaclav Kotesovec, Jun 03 2018

MATHEMATICA

terms = 12;

E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];

E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];

E6[x]/E8[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 23 2018 *)

CROSSREFS

Cf. A008410 (E_8). A013973 (E_6), A287933, A288840.

E_k/E_{k+2}: A294181 (k=2), A294182 (k=4), this sequence (k=6).

Sequence in context: A249216 A289063 A289061 * A288840 A289417 A131640

Adjacent sequences:  A294180 A294181 A294182 * A294184 A294185 A294186

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 11 2018

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)