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 A112213 McKay-Thompson series of class 88A for the Monster group. 1

%I

%S 1,1,0,1,1,1,1,1,2,2,2,3,4,3,4,5,6,6,6,8,9,10,10,12,14,15,16,19,21,22,

%T 24,27,31,34,36,40,46,48,52,58,64,69,74,82,91,98,104,115,127,136,145,

%U 159,174,186,200,218,238,254,272,296,322,343,366,398,430,460,492,531

%N McKay-Thompson series of class 88A for the Monster group.

%C Also McKay-Thompson series of class 88B for Monster. - _Michel Marcus_, Feb 19 2014

%H G. C. Greubel, <a href="/A112213/b112213.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>, Commun. 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 q^(1/2)*((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4)*eta(q^11)* eta(q^44))) in powers of q. - _G. C. Greubel_, Jul 02 2018

%F a(n) ~ exp(sqrt(2*n/11)*Pi) / (2^(5/4) * 11^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018

%e T88A = 1/q +q +q^5 +q^7 +q^9 +q^11 +q^13 +2*q^15 +2*q^17 +...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*((eta[q^2]*eta[q^22])^2/ (eta[q]*eta[q^4]*eta[q^11]*eta[q^44])); a:= CoefficientList[Series[A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 02 2018 *)

%o (PARI) q='q+O('q^70); A = ((eta(q^2)*eta(q^22))^2/(eta(q)*eta(q^4) *eta(q^11)*eta(q^44))); Vec(A) \\ _G. C. Greubel_, Jul 02 2018

%K nonn

%O 0,9

%A _Michael Somos_, Aug 28 2005

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Last modified February 20 15:04 EST 2019. Contains 320327 sequences. (Running on oeis4.)