A289562 - OEIS

A289562

Coefficients of 1/(q*(j(q)-1728))^3 where j(q) is the elliptic modular invariant.

1, 2952, 5218884, 7138351488, 8319960432666, 8678332561127616, 8338315178481134040, 7518590274496806176256, 6444205834302869333758299, 5298802621872639665867604832, 4208666443076672300677008045636, 3246069554930472099322915758511872

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..362

FORMULA

G.f.: Product_{n>=1} (1-q^n)^(-3*A289061(n)).

a(n) ~ c * exp(2*Pi*n) * n^5, where c = Gamma(3/4)^24 * exp(6*Pi) / (4081466880 * Pi^6) = 0.0051446247390864841578336638645072392120317488530740050289688... - Vaclav Kotesovec, Mar 07 2018

MATHEMATICA

CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-3), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)

CROSSREFS

(q*(j(q)-1728))^(k/24): A289563 (k=-96), this sequence (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).

Cf. A289061.

Sequence in context: A025514 A204393 A178273 * A054833 A054212 A179138

Adjacent sequences: A289559 A289560 A289561 * A289563 A289564 A289565

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 08 2017

STATUS

approved