|
|
A058644
|
|
McKay-Thompson series of class 36A for Monster.
|
|
6
|
|
|
1, 0, 3, 2, 3, 6, 10, 12, 15, 22, 30, 36, 44, 60, 78, 96, 117, 150, 190, 228, 276, 340, 420, 504, 603, 732, 885, 1052, 1245, 1488, 1770, 2088, 2454, 2902, 3420, 3996, 4666, 5460, 6378, 7400, 8583, 9972, 11566, 13344, 15378, 17752, 20448, 23472, 26904, 30876
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017
|
|
EXAMPLE
|
T36A = 1/q + 3*q + 2*q^2 + 3*q^3 + 6*q^4 + 10*q^5 + 12*q^6 + 15*q^7 + ...
|
|
MATHEMATICA
|
eta[q_]:= q^(1/24)*QPochhammer[q]; e36B2:= eta[q]*eta[q^4]*eta[q^18]/( eta[q^2]*eta[q^9]*eta[q^36]); T36A := 1 +e36B2 +3/e36B2; a:= CoefficientList[Series[q*T36A, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, May 09 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); Vec(1 + (eta(q)*eta(q^4)*eta(q^18)/(eta(q^2) *eta(q^9)*eta(q^36)))/q + 3*q*(eta(q^2)*eta(q^9)*eta(q^36)/(eta(q) *eta(q^4)*eta(q^18)))) \\ G. C. Greubel, May 09 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|