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A289318 Coefficients in expansion of E_4^(3/4). 8
1, 180, -3780, 447840, -59046660, 8921092680, -1463828444640, 253953515257920, -45858209756343300, 8534765953624978260, -1626301691950399586280, 315807346469727624396960, -62284193156782292089690080, 12443904711281870749228431240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..425

FORMULA

G.f.: Product_{n>=1} (1-q^n)^(3*A110163(n)/4).

a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(7/4), where c = 3^(5/2) * Gamma(1/3)^(27/2) / (256 * 2^(3/4) * Pi^9 * Gamma(1/4)) = 0.2007048471908800363193160136812560289856774734680572658944418664975... - Vaclav Kotesovec, Jul 08 2017, updated Mar 05 2018

MATHEMATICA

nmax = 20; CoefficientList[Series[(1 + 240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^(3/4), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

CROSSREFS

E_4^(k/8): A108091 (k=1), A289307 (k=2), A289308 (k=3), A289292 (k=4), A289309 (k=5), this sequence (k=6), A289319 (k=7).

Cf. A004009 (E_4), A110163.

Sequence in context: A112068 A058835 A008432 * A250146 A243465 A271673

Adjacent sequences:  A289315 A289316 A289317 * A289319 A289320 A289321

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 02 2017

STATUS

approved

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Last modified October 26 21:33 EDT 2021. Contains 348269 sequences. (Running on oeis4.)