|
|
A289417
|
|
Coefficients of 1/(q*(j(q)-1728)) where j(q) is the elliptic modular invariant.
|
|
10
|
|
|
1, 984, 771372, 543802432, 361216628430, 230920762687776, 143732944930479800, 87718753215371355648, 52729710063184125105381, 31319171802847165756090320, 18421996714811488321383528228, 10748837396953435386200311855872
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Product_{n>=1} (1-q^n)^(-A289061(n)).
a(n) ~ c * exp(2*Pi*n) * n, where c = Gamma(3/4)^8 * exp(2*Pi) / (324 * Pi^2) = 0.851487576721136974981670736748581778120097667011853803210435262759745... - Vaclav Kotesovec, Mar 07 2018
|
|
MATHEMATICA
|
CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-1), {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), this sequence (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).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|