|
|
A058579
|
|
McKay-Thompson series of class 24I for Monster.
|
|
2
|
|
|
1, 0, 4, 6, 11, 18, 28, 42, 62, 90, 128, 180, 250, 342, 464, 624, 831, 1098, 1440, 1878, 2432, 3132, 4012, 5112, 6485, 8190, 10300, 12900, 16097, 20016, 24804, 30636, 37724, 46314, 56700, 69228, 84302, 102402, 124088, 150024, 180973, 217836
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,3
|
|
LINKS
|
|
|
FORMULA
|
Expansion of -1 + (eta(q^4)^4*eta(q^6)^4)/(eta(q)*eta(q^2)^2*eta(q^3) *eta(q^8)*eta(q^12)^2*eta(q^24)) in powers of q. - G. C. Greubel, Jun 18 2018
a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
|
|
EXAMPLE
|
T24I = 1/q + 4*q + 6*q^2 + 11*q^3 + 18*q^4 + 28*q^5 + 42*q^6 + 62*q^7 + ...
|
|
MATHEMATICA
|
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^4]^4*eta[q^6]^4)/(eta[q]* eta[q^2]^2*eta[q^3]*eta[q^8]*eta[q^12]^2*eta[q^24]); a:=CoefficientList[ Series[-1 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); A = -1 + (eta(q^4)^4*eta(q^6)^4)/(eta(q)*eta(q^2)^2 *eta(q^3)*eta(q^8)*eta(q^12)^2*eta(q^24))/q; Vec(A) \\ G. C. Greubel, Jun 18 2018
|
|
CROSSREFS
|
Cf. A138688 (same sequence except for n=0).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|