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A289319 Coefficients in expansion of E_4^(7/8). 8
1, 210, -1260, 232680, -28907970, 4211355960, -671557897080, 113817372354240, -20151698294479500, 3687092782592216970, -692109989731133096760, 132609267059636375116920, -25838624519733523814390760, 5105657091664960508653858680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, for 0 < m < 1, the expansion of (E_4)^m is asymptotic to (-1)^(n+1) * m * 3^(2*m) * Gamma(1/3)^(18*m) * exp(Pi*sqrt(3)*n) / (2^(9*m) * Pi^(12*m) * Gamma(1-m) * n^(1+m)). - Vaclav Kotesovec, Mar 05 2018

LINKS

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

FORMULA

G.f.: Product_{n>=1} (1-q^n)^(7*A110163(n)/8).

a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(15/8), where c = 7 * 3^(7/4) * Gamma(1/3)^(63/4) / (1024 * 2^(7/8) * Pi^(21/2) * Gamma(1/8)) = 0.1121182787986009012644546699220584282491804117887058146553161217384... - 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}])^(7/8), {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), A289318 (k=6), this sequence (k=7).

Cf. A004009 (E_4), A110163.

Sequence in context: A235241 A046302 A217532 * A157408 A333771 A118281

Adjacent sequences:  A289316 A289317 A289318 * A289320 A289321 A289322

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 02 2017

STATUS

approved

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Last modified October 28 10:48 EDT 2021. Contains 348327 sequences. (Running on oeis4.)