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A289563 Coefficients of 1/(q*(j(q)-1728))^4 where j(q) is the elliptic modular invariant. 6
1, 3936, 8895024, 15094625920, 21336320693400, 26506772152211520, 29887990556174431424, 31237788209244729015552, 30709242534935581933885740, 28700724444538653431660487520, 25706227251014342788669659769056, 22202613798662970539127791744222592 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{n>=1} (1-q^n)^(-4*A289061(n)).
a(n) ~ c * exp(2*Pi*n) * n^7, where c = Gamma(3/4)^32 * exp(8*Pi) / (55540601303040 * Pi^8) = 0.0001042996202910562374208781457852661312263780276025385904... - Vaclav Kotesovec, Mar 07 2018
MATHEMATICA
CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-4), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)
CROSSREFS
(q*(j(q)-1728))^(k/24): this sequence (k=-96), A289562 (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: A251823 A031822 A288894 * A198641 A045232 A252455
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 08 2017
STATUS
approved

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Last modified February 25 09:03 EST 2024. Contains 370310 sequences. (Running on oeis4.)