cp's OEIS Frontend

A289416 Coefficients of (q*(j(q)-1728))^(-1/24) where j(q) is the elliptic modular invariant.

%I A289416 #17 Mar 07 2018 17:13:46
%S A289416 1,41,12809,4767210,1969719570,861799083811,391094324350380,
%T A289416 182038077972154741,86322373755372340110,41521193849940130872000,
%U A289416 20197774625594843441436930,9915082544034345319047507780
%N A289416 Coefficients of (q*(j(q)-1728))^(-1/24) where j(q) is the elliptic modular invariant.
%H A289416 Seiichi Manyama, <a href="/A289416/b289416.txt">Table of n, a(n) for n = 0..367</a>
%F A289416 G.f.: Product_{n>=1} (1-q^n)^(-A289061(n)/24) = Product_{n>=1} (1-q^n)^(1-A289396(n)).
%F A289416 a(n) ~ c * exp(2*Pi*n) / n^(11/12), where c = Gamma(3/4)^(1/3) * exp(Pi/12) / (2^(1/12) * 3^(1/6) * Pi^(1/12) * Gamma(1/12)) = 0.086380262154841817375196725... - _Vaclav Kotesovec_, Mar 07 2018
%t A289416 CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-1/24), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)
%Y A289416 (q*(j(q)-1728))^(k/24): A289563 (k=-96), A289562 (k=-72), A289561 (k=-48), A289417 (k=-24), this sequence (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).
%K A289416 nonn
%O A289416 0,2
%A A289416 _Seiichi Manyama_, Jul 06 2017