A106203 Coefficients of ((j(q)-1728)q)^(1/24) where j(q) is the elliptic modular invariant.

1, -41, -11128, -3785793, -1476507895, -618962022329, -271503819749095, -122857395553223337, -56870247894888518054, -26784343611333662213130, -12787694574831980406719382, -6172809198874485994313412898

Offset: 0

Author

Michael Somos, Apr 25 2005

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..367

Crossrefs

(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).

Cf. A000521, A289061.

Programs

Mathematica

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 *)

PARI

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

Formula

G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/24). - Seiichi Manyama, Jul 02 2017

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