|
|
A058504
|
|
McKay-Thompson series of class 14C for Monster.
|
|
2
|
|
|
1, 0, 10, 24, 51, 100, 190, 340, 585, 984, 1606, 2564, 4022, 6188, 9382, 14044, 20746, 30308, 43836, 62784, 89153, 125588, 175542, 243656, 335988, 460388, 627178, 849676, 1145024, 1535416, 2049200, 2722544, 3601681, 4745208, 6227276, 8141656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,3
|
|
LINKS
|
|
|
FORMULA
|
Expansion of -4 + (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14)))^4 in powers of q. - G. C. Greubel, Jun 14 2018
a(n) ~ exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
|
|
EXAMPLE
|
T14C = 1/q + 10*q + 24*q^2 + 51*q^3 + 100*q^4 + 190*q^5 + 340*q^6 + ...
|
|
MATHEMATICA
|
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-4 + (eta[q^2]*eta[q^7]/(eta[q]*eta[q^14]))^4), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 14 2018 *)
|
|
PROG
|
(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^7)/(eta(q)*eta(q^14)))^4/q; Vec(A - 4) \\ G. C. Greubel, Jun 14 2018
|
|
CROSSREFS
|
Cf. A128516 (same sequence except for n=0).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|