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A112174 McKay-Thompson series of class 36d for the Monster group. 1

%I

%S 1,1,0,2,-2,0,3,1,0,4,0,0,5,0,0,8,-2,0,11,4,0,16,-4,0,21,4,0,26,-2,0,

%T 34,1,0,44,-4,0,58,9,0,74,-12,0,93,9,0,116,-4,0,143,5,0,178,-12,0,221,

%U 20,0,272,-24,0,332,20,0,402,-14,0,487,13,0,588,-24,0,710,42,0,854,-50,0,1021,42,0

%N McKay-Thompson series of class 36d for the Monster group.

%H G. C. Greubel, <a href="/A112174/b112174.txt">Table of n, a(n) for n = 0..2500</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 A + q/A, where A = q^(1/2)*(eta(q^6)*eta(q^9)/( eta(q^3)* eta(q^18)))^2, in powers of q. - _G. C. Greubel_, Jun 26 2018

%e T36d = 1/q +q +2*q^5 -2*q^7 +3*q^11 +q^13 +4*q^17 +5*q^23 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^9]/( eta[q^3]*eta[q^18]))^2; a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 26 2018 *)

%o (PARI) q='q+O('q^80); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^2; Vec(A+ q/A) \\ _G. C. Greubel_, Jun 26 2018

%K sign

%O 0,4

%A _Michael Somos_, Aug 28 2005

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Last modified November 22 08:33 EST 2019. Contains 329389 sequences. (Running on oeis4.)