|
|
A112152
|
|
McKay-Thompson series of class 16c for the Monster group.
|
|
1
|
|
|
1, -4, -2, -8, -1, -20, 2, -40, 3, -72, -2, -128, -4, -220, 4, -360, 5, -576, -8, -904, -8, -1384, 10, -2088, 11, -3108, -12, -4552, -15, -6592, 18, -9448, 22, -13392, -26, -18816, -29, -26216, 34, -36224, 38, -49700, -42, -67728, -51, -91688, 56, -123392, 66, -165128, -78, -219784, -85, -291072
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Expansion of A - 4*q/A, where A = q^(1/2)*(eta(q^2)/eta(q^8))^2, in powers of q. - G. C. Greubel, Jun 26 2018
|
|
EXAMPLE
|
T16c = 1/q -4*q -2*q^3 -8*q^5 -q^7 -20*q^9 +2*q^11 -40*q^13 +...
|
|
MATHEMATICA
|
eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]/eta[q^8])^2; a:= CoefficientList[Series[A - 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); A = (eta(q^2)/eta(q^8))^2; Vec(A -4*q/A) \\ G. C. Greubel, Jun 26 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|