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A289334 Coefficients of (q*(j(q)-1728))^(1/4) where j(q) is the elliptic modular invariant. 15

%I #14 Mar 07 2018 17:17:47

%S 1,-246,-41553,-10405738,-3425019885,-1274958998550,-510099547824244,

%T -214102720094848884,-92997705562440483771,-41448768067643091078680,

%U -18848488732890018582016056,-8710420728901868885695224690

%N Coefficients of (q*(j(q)-1728))^(1/4) where j(q) is the elliptic modular invariant.

%H Seiichi Manyama, <a href="/A289334/b289334.txt">Table of n, a(n) for n = 0..367</a>

%F G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/4).

%F a(n) ~ c * exp(2*Pi*n) / n^(3/2), where c = -3 * exp(-Pi/2) / (2^(1/2) * Gamma(3/4)^2) = -0.293663850547434552890056440879436571786655817166913678971... - _Vaclav Kotesovec_, Mar 07 2018

%t CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/4), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)

%Y (q*(j(q)-1728))^(k/24): A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), this sequence (k=6), A007242 (k=12), A289063 (k=24).

%Y Cf. A289061.

%K sign

%O 0,2

%A _Seiichi Manyama_, Jul 02 2017

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)