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 A112180 McKay-Thompson series of class 40a for the Monster group. 1

%I

%S 1,0,3,4,4,4,7,12,13,16,22,28,38,44,55,72,83,104,129,156,187,220,273,

%T 328,384,452,539,652,757,880,1041,1220,1428,1652,1924,2244,2585,2992,

%U 3458,3992,4581,5244,6053,6936,7910,9024,10303,11784,13380,15176

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

%H G. C. Greubel, <a href="/A112180/b112180.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 A - q/A, where A = q^(1/2)*(eta(q^4)*eta(q^5)/( eta(q)* eta(q^20))), in powers of q. - _G. C. Greubel_, Jun 26 2018

%F a(n) ~ exp(Pi*sqrt(2*n/5)) / (2^(5/4) * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 27 2018

%e T40a = 1/q +3*q^3 +4*q^5 +4*q^7 +4*q^9 +7*q^11 +12*q^13 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^5]/( eta[q]*eta[q^20])); 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^50); A = eta(q^4)*eta(q^5)/(eta(q)*eta(q^20)); Vec(A - q/A) \\ _G. C. Greubel_, Jun 26 2018

%K nonn

%O 0,3

%A _Michael Somos_, Aug 28 2005

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Last modified March 18 19:58 EDT 2019. Contains 321293 sequences. (Running on oeis4.)