|
|
A112155
|
|
McKay-Thompson series of class 16h for the Monster group.
|
|
1
|
|
|
1, -2, 2, 4, 3, -2, 6, 4, 7, -12, 10, 16, 16, -14, 20, 20, 29, -40, 40, 52, 52, -52, 70, 68, 91, -114, 116, 148, 149, -152, 190, 196, 242, -296, 306, 368, 383, -396, 478, 496, 590, -698, 730, 856, 897, -940, 1096, 1152, 1342, -1548, 1630, 1876, 1975, -2080, 2390, 2516
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Expansion of A - 2*q/A, where A = q^(1/2)*(eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2, in powers of q. - G. C. Greubel, Jun 28 2018
|
|
EXAMPLE
|
T16h = 1/q - 2*q + 2*q^3 + 4*q^5 + 3*q^7 - 2*q^9 + 6*q^11 + 4*q^13 + ...
|
|
MATHEMATICA
|
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^8]/( eta[q^2]*eta[q^16]))^2; a:= CoefficientList[Series[A - 2*q/A, {q, 0, n}]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 28 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); A = (eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2; Vec(A - 2*q/A) \\ G. C. Greubel, Jun 28 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|