|
|
A058659
|
|
McKay-Thompson series of class 39A for Monster.
|
|
2
|
|
|
1, 0, 3, 1, 3, 6, 6, 9, 15, 15, 21, 30, 34, 42, 60, 66, 84, 108, 127, 153, 201, 226, 276, 342, 400, 471, 585, 667, 795, 954, 1103, 1290, 1551, 1771, 2073, 2442, 2807, 3246, 3816, 4346, 5028, 5838, 6662, 7638, 8856, 10040, 11505, 13212, 14991, 17064, 19560
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,3
|
|
LINKS
|
|
|
FORMULA
|
Expansion of A - 1 + 1/A, where A = (eta(q^3)*eta(q^13)/(eta(q)* eta(q^39))), in powers of q. - G. C. Greubel, Jun 23 2018
a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018
|
|
EXAMPLE
|
T39A = 1/q + 3*q + q^2 + 3*q^3 + 6*q^4 + 6*q^5 + 9*q^6 + 15*q^7 + 15*q^8 + ...
|
|
MATHEMATICA
|
eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^13]/( eta[q]* eta[q^39])); a := CoefficientList[Series[A - 1 + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); A = eta(q^3)*eta(q^13)/(q*eta(q)*eta(q^39)); Vec(A - 1 +1/A) \\ G. C. Greubel, Jun 23 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|