A289309 Coefficients in expansion of E_4^(5/8).

1, 150, -5400, 625200, -86672550, 13570016400, -2289741037200, 406440122001600, -74830416797043000, 14162747887897808550, -2738995393669565720400, 538973037306449327998800, -107578899914865970323788400, 21729813219122500082762389200

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1-q^n)^(5*A110163(n)/8).

a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(13/8), where c = 5 * 3^(5/4) * Gamma(1/3)^(45/4) / (256 * 2^(5/8) * Pi^(15/2) * Gamma(3/8)) = 0.2571085249207580781634342667473393997795373224370302803101380883544... - 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}])^(5/8), {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), this sequence (k=5), A289318 (k=6), A289319 (k=7).

Cf. A004009 (E_4), A110163.

Sequence in context: A128963 A293097 A185406 * A337032 A250537 A264065

Adjacent sequences: A289306 A289307 A289308 * A289310 A289311 A289312

Keyword

sign

Author

Seiichi Manyama, Jul 02 2017

Status

approved