A289563 - OEIS

%I #16 Mar 07 2018 17:11:17

%S 1,3936,8895024,15094625920,21336320693400,26506772152211520,

%T 29887990556174431424,31237788209244729015552,

%U 30709242534935581933885740,28700724444538653431660487520,25706227251014342788669659769056,22202613798662970539127791744222592

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

%H Seiichi Manyama, <a href="/A289563/b289563.txt">Table of n, a(n) for n = 0..361</a>

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

%F a(n) ~ c * exp(2*Pi*n) * n^7, where c = Gamma(3/4)^32 * exp(8*Pi) / (55540601303040 * Pi^8) = 0.0001042996202910562374208781457852661312263780276025385904... - _Vaclav Kotesovec_, Mar 07 2018

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

%Y (q*(j(q)-1728))^(k/24): this sequence (k=-96), A289562 (k=-72), A289561 (k=-48), A289417 (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 Cf. A289061.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 08 2017