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A289417 Coefficients of 1/(q*(j(q)-1728)) where j(q) is the elliptic modular invariant.

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%I A289417 #23 Mar 07 2018 17:12:55
%S A289417 1,984,771372,543802432,361216628430,230920762687776,
%T A289417 143732944930479800,87718753215371355648,52729710063184125105381,
%U A289417 31319171802847165756090320,18421996714811488321383528228,10748837396953435386200311855872
%N A289417 Coefficients of 1/(q*(j(q)-1728)) where j(q) is the elliptic modular invariant.
%H A289417 Seiichi Manyama, <a href="/A289417/b289417.txt">Table of n, a(n) for n = 0..365</a>
%F A289417 G.f.: Product_{n>=1} (1-q^n)^(-A289061(n)).
%F A289417 a(n) ~ c * exp(2*Pi*n) * n, where c = Gamma(3/4)^8 * exp(2*Pi) / (324 * Pi^2) = 0.851487576721136974981670736748581778120097667011853803210435262759745... - _Vaclav Kotesovec_, Mar 07 2018
%t A289417 CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-1), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)
%Y A289417 (q*(j(q)-1728))^(k/24): A289563 (k=-96), A289562 (k=-72), A289561 (k=-48), this sequence (k=-24), A289416 (k=-1), A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), A289334 (k=6), A007242 (k=12), A289063 (k=24).
%Y A289417 Cf. A289061, A289209.
%K A289417 nonn
%O A289417 0,2
%A A289417 _Seiichi Manyama_, Jul 06 2017