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 A112183 McKay-Thompson series of class 40e for the Monster group. 1

%I

%S 1,1,-1,1,0,1,0,-1,0,0,2,2,-1,1,0,2,1,-1,1,0,4,3,-3,2,0,4,2,-3,1,0,7,

%T 5,-5,4,0,7,4,-5,3,0,12,9,-8,6,0,13,7,-9,5,0,19,14,-13,9,0,21,12,-14,

%U 8,0,31,22,-21,15,0,34,19,-23,13,0,47,33,-31,22,0,52,31,-35,21,0,71,49,-48,33,0,79,47

%N McKay-Thompson series of class 40e for the Monster group.

%H G. C. Greubel, <a href="/A112183/b112183.txt">Table of n, a(n) for n = 0..1500</a>

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

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

%F Expansion of (T10b + 4)^(1/4), where T10b = A058103, in powers of q. - _G. C. Greubel_, Jun 28 2018

%e T40e = 1/q +q^3 -q^7 +q^11 +q^19 -q^27 +2*q^39 +2*q^43 -q^47 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 120; A:= eta[q]/eta[q^25]; B:= (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]); c:= ((eta[q]*eta[q^2])/( eta[q^5]*eta[q^10]))^2; f5 := (c /. {q -> q^5}); T10b := (2 + c + 5*(c/A^2)*(1 - 1/B)^2 + 25/f5); a:= CoefficientList[Series[ (q*(T10b + 4) + O[q]^nmax)^(1/4), {q, 0, 110}], q]; Table[a[[n]], {n, 1, 100}] (* _G. C. Greubel_, Jun 28 2018 *)

%K sign

%O 0,11

%A _Michael Somos_, Aug 28 2005

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Last modified September 25 06:05 EDT 2020. Contains 337335 sequences. (Running on oeis4.)