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 A112220 McKay-Thompson series of class 117a for the Monster group. 1

%I

%S 1,1,0,0,1,0,1,1,1,1,2,1,2,2,2,2,3,2,3,4,3,4,5,4,6,6,6,7,8,7,9,10,10,

%T 11,13,12,15,16,16,18,21,19,23,25,25,28,31,30,35,38,38,42,47,46,52,56,

%U 57,62,69,68,77,82,84,91,100,100,111,118,121,131,142,144,158,168,173

%N McKay-Thompson series of class 117a for the Monster group.

%H G. C. Greubel, <a href="/A112220/b112220.txt">Table of n, a(n) for n = 0..1000</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 (T39A + 3)^(1/3) in powers of q, where T39A = A058659. - _G. C. Greubel_, Jul 02 2018

%F a(n) ~ exp(4*Pi*sqrt(n/13)/3) / (sqrt(6) * 13^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018

%e T117a = 1/q +q^2 +q^11 +q^17 +q^20 +q^23 +q^26 +2*q^29 +q^32 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; c:= (eta[q^3]*eta[q^13]/ (eta[q]*eta[q^39])); T39A := c + 1/c - 1; a:= CoefficientList[Series[ (q*T39A + 3*q + O[q]^nmax)^(1/3), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jul 02 2018 *)

%o (PARI) seq(n)={my(x=x+O(x*x^n)); my(A=eta(x^3)*eta(x^13)/(x*eta(x)*eta(x^39))); Vec((x*(2 + A + 1/A))^(1/3))} \\ _Andrew Howroyd_, Jul 02 2018

%Y Cf. A058659.

%K nonn

%O 0,11

%A _Michael Somos_, Aug 28 2005

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)