|
|
A058637
|
|
McKay-Thompson series of class 33B for Monster.
|
|
2
|
|
|
1, 0, 2, 4, 5, 6, 14, 14, 20, 30, 37, 46, 71, 82, 108, 144, 173, 218, 291, 340, 425, 540, 647, 788, 996, 1170, 1427, 1744, 2072, 2476, 3019, 3536, 4224, 5058, 5942, 7008, 8363, 9734, 11453, 13512, 15719, 18340, 21546, 24908, 28983, 33774, 38995, 45086, 52353
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,3
|
|
LINKS
|
|
|
FORMULA
|
Expansion of A + 1 + 3/A, where A =eta(q)*eta(q^11)/(eta(q^3)*eta(q^33)), in powers of q. - G. C. Greubel, Jun 23 2018
a(n) ~ exp(4*Pi*sqrt(n/33)) / (sqrt(2) * 33^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
|
|
EXAMPLE
|
T33B = 1/q + 2*q + 4*q^2 + 5*q^3 + 6*q^4 + 14*q^5 + 14*q^6 + 20*q^7 + ...
|
|
MATHEMATICA
|
eta[q_] := q^(1/24)*QPochhammer[q]; A := eta[q]*eta[q^11]/( eta[q^3]* eta[q^33]); a:= CoefficientList[Series[q*(A + 1 + 3/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)*eta(q^11)/(q*eta(q^3)*eta(q^33)); Vec(A + 1 + 3/A) \\ G. C. Greubel, Jun 23 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|