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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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.

Index entries for McKay-Thompson series for Monster simple group

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

Cf. A045485, A121665.

Sequence in context: A317412 A231393 A231461 * A003913 A251321 A074089

Adjacent sequences:  A007252 A007253 A007254 * A007256 A007257 A007258

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)