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A289561 Coefficients of 1/(q*(j(q)-1728))^2 where j(q) is the elliptic modular invariant. 6
1, 1968, 2511000, 2605664960, 2387651205420, 2011663789279200, 1594903822090229312, 1207416525204065938560, 881461062200198781904590, 624887481909094711741279120, 432393768184906363401468637728, 293171504960988659691658645670592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..363

FORMULA

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

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

MATHEMATICA

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 *)

CROSSREFS

(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).

Cf. A289061.

Sequence in context: A193312 A202596 A239185 * A256738 A252012 A250804

Adjacent sequences:  A289558 A289559 A289560 * A289562 A289563 A289564

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 08 2017

STATUS

approved

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Last modified June 13 03:45 EDT 2021. Contains 344980 sequences. (Running on oeis4.)