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A112210 McKay-Thompson series of class 82a for the Monster group. 1

%I

%S 1,0,1,1,1,1,2,2,2,2,3,3,4,4,5,6,7,7,9,9,11,12,14,15,18,19,22,24,27,

%T 29,34,36,41,44,50,54,61,65,73,79,88,95,106,114,126,136,150,162,179,

%U 192,211,228,249,268,294,316,345,371,404,434,473,507,551,592,641,688

%N McKay-Thompson series of class 82a for the Monster group.

%H G. C. Greubel, <a href="/A112210/b112210.txt">Table of n, a(n) for n = -1..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 G(q^41)*H(q) - q^8*H(q^41)*G(q) in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - _G. C. Greubel_, Jul 02 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/41)) / (2^(3/4) * 41^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018

%e T82a = 1/q +q^3 +q^5 +q^7 +q^9 +2*q^11 +2*q^13 +2*q^15 +2*q^17 +...

%t QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2];

%t B := G[x^41]*H[x] - x^8*H[x^41]*G[x]; a:= CoefficientList[Series[B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 02 2018 *)

%K nonn

%O -1,7

%A _Michael Somos_, Aug 28 2005

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Last modified November 17 06:06 EST 2019. Contains 329217 sequences. (Running on oeis4.)