A289561 - OEIS

%I #15 Mar 07 2018 17:12:20

%S 1,1968,2511000,2605664960,2387651205420,2011663789279200,

%T 1594903822090229312,1207416525204065938560,881461062200198781904590,

%U 624887481909094711741279120,432393768184906363401468637728,293171504960988659691658645670592

%N Coefficients of 1/(q*(j(q)-1728))^2 where j(q) is the elliptic modular invariant.

%H Seiichi Manyama, <a href="/A289561/b289561.txt">Table of n, a(n) for n = 0..363</a>

%F G.f.: Product_{n>=1} (1-q^n)^(-2*A289061(n)).

%F a(n) ~ c * exp(2*Pi*n) * n^3, where c = Gamma(3/4)^16 * exp(4*Pi) / (629856 * Pi^4) = 0.120838515551739021017044909469013807578104459775498957232984908667972... - _Vaclav Kotesovec_, Mar 07 2018

%t CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-2), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *)

%Y (q*(j(q)-1728))^(k/24): A289563 (k=-96), A289562 (k=-72), this sequence (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