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

1, 41, 12809, 4767210, 1969719570, 861799083811, 391094324350380, 182038077972154741, 86322373755372340110, 41521193849940130872000, 20197774625594843441436930, 9915082544034345319047507780

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1-q^n)^(-A289061(n)/24) = Product_{n>=1} (1-q^n)^(1-A289396(n)).

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

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 *)

Crossrefs

(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).

Sequence in context: A240704 A240641 A106203 * A199255 A199200 A198602

Adjacent sequences: A289413 A289414 A289415 * A289417 A289418 A289419

Keyword

nonn

Author

Seiichi Manyama, Jul 06 2017

Status

approved