A106203 - OEIS

%I #21 Mar 07 2018 17:14:38

%S 1,-41,-11128,-3785793,-1476507895,-618962022329,-271503819749095,

%T -122857395553223337,-56870247894888518054,-26784343611333662213130,

%U -12787694574831980406719382,-6172809198874485994313412898

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

%H Seiichi Manyama, <a href="/A106203/b106203.txt">Table of n, a(n) for n = 0..367</a>

%F G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/24). - _Seiichi Manyama_, Jul 02 2017

%F a(n) ~ c * exp(2*Pi*n) / n^(13/12), where c = -2^(1/12) * Pi^(25/12) * exp(-Pi/12) / (3^(13/12) * Gamma(2/3)^2 * Gamma(3/4)^(7/3) * Gamma(1/12)) = -0.0794786705643291777786030631826408355507134016936764993676699378963... - _Vaclav Kotesovec_, Mar 07 2018

%t 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 *)

%o (PARI) {a(n)=if(n<0,0, polcoeff( ((ellj(x+x^2*O(x^n))-1728)*x)^(1/24),n))}

%Y (q*(j(q)-1728))^(k/24): A289563 (k=-96), A289562 (k=-72), A289561 (k=-48), A289417 (k=-24), A289416 (k=-1), this sequence (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. A000521, A289061.

%K sign

%O 0,2

%A _Michael Somos_, Apr 25 2005