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A007255
McKay-Thompson series of class 6B for Monster.
(Formerly M5354)
3
1, 0, 78, 364, 1365, 4380, 12520, 32772, 80094, 185276, 409578, 871272, 1792754, 3582708, 6977100, 13277472, 24747867, 45267324, 81389908, 144048396, 251265288, 432425864, 734953116, 1234647216, 2051576037
OFFSET
-1,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
I. Chen and N. Yui, Singular values of Thompson series. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters, Comm. Algebra 18 (1990), no. 1, 253-278.
FORMULA
a(n) = A045485(n) = A121665(n) apart from n=0. - Sean A. Irvine, Nov 26 2017
a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 26 2018
EXAMPLE
T6B = 1/q + 78*q + 364*q^2 + 1365*q^3 + 4380*q^4 + 12520*q^5 + 32772*q^6 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(-12 + (eta[q^2]*eta[q^3]/(eta[q]*eta[q^6]))^12), {q, 0, 60}], q];
Table[A007255[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 12 2018 *)
PROG
(PARI) q='q+O('q^30); A=-12+(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12/q; Vec(A) \\ G. C. Greubel, Jun 12 2018
CROSSREFS
Sequence in context: A317412 A231393 A231461 * A003913 A251321 A074089
KEYWORD
nonn
STATUS
approved