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A007255 McKay-Thompson series of class 6B for Monster.
(Formerly M5354)
3

%I M5354 #27 Jun 26 2018 08:40:19

%S 1,0,78,364,1365,4380,12520,32772,80094,185276,409578,871272,1792754,

%T 3582708,6977100,13277472,24747867,45267324,81389908,144048396,

%U 251265288,432425864,734953116,1234647216,2051576037

%N McKay-Thompson series of class 6B for Monster.

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

%H G. C. Greubel, <a href="/A007255/b007255.txt">Table of n, a(n) for n = -1..1000</a>

%H I. Chen and N. Yui, <a href="http://www.math.sfu.ca/~ichen/pub.html">Singular values of Thompson series</a>. 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.

%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F a(n) = A045485(n) = A121665(n) apart from n=0. - _Sean A. Irvine_, Nov 26 2017

%F a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018

%e T6B = 1/q + 78*q + 364*q^2 + 1365*q^3 + 4380*q^4 + 12520*q^5 + 32772*q^6 + ...

%t 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];

%t Table[A007255[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 12 2018 *)

%o (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

%Y Cf. A045485, A121665.

%K nonn

%O -1,3

%A _N. J. A. Sloane_

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)