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A299829 Coefficients in expansion of (q*j(q))^(-5/24) where j(q) is the elliptic modular invariant (A000521). 2

%I

%S 1,-155,28655,-5760440,1202381535,-256382973906,55428428962345,

%T -12099932165757725,2660417880657190215,-588191792902675685120,

%U 130616050711284314803809,-29108986917589590736384395,6506478780288042396481955095

%N Coefficients in expansion of (q*j(q))^(-5/24) where j(q) is the elliptic modular invariant (A000521).

%F Convolution inverse of A289300.

%F a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(3/8), where c = 0.730428963078390701326735403005831754545040392327211512089... = 2^(5/8) * exp(5 * Pi / (8 * sqrt(3))) * Pi^(5/2) / (3^(5/8) * Gamma(1/3)^(15/4) * Gamma(5/8)). - _Vaclav Kotesovec_, Feb 20 2018, updated Mar 06 2018

%F a(n) * A289300(n) ~ -5*sqrt(2 + sqrt(2)) * exp(2*sqrt(3)*Pi*n) / (16*Pi*n^2). - _Vaclav Kotesovec_, Feb 20 2018

%t CoefficientList[Series[(2 * QPochhammer[-1, x])^5 / (65536 + x*QPochhammer[-1, x]^24)^(15/24), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 20 2018 *)

%Y Cf. A000521, A289300.

%K sign

%O 0,2

%A _Seiichi Manyama_, Feb 20 2018

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Last modified July 21 02:02 EDT 2019. Contains 325189 sequences. (Running on oeis4.)