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A112160 McKay-Thompson series of class 24E for the Monster group.

%I A112160 #24 Jul 02 2018 01:49:24
%S A112160 1,4,6,8,17,28,38,56,84,124,172,232,325,448,594,784,1049,1388,1796,
%T A112160 2320,3005,3864,4912,6216,7877,9940,12430,15488,19309,23972,29580,
%U A112160 36408,44766,54876,66978,81536,99150,120272,145374,175344,211242
%N A112160 McKay-Thompson series of class 24E for the Monster group.
%H A112160 G. C. Greubel, <a href="/A112160/b112160.txt">Table of n, a(n) for n = 0..1000</a>
%H A112160 D. Ford, J. McKay and S. P. Norton, <a href="https://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%H A112160 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A112160 a(n) ~ exp(Pi*sqrt(2*n/3)) / (2 * 6^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 27 2015
%F A112160 Expansion of q^(1/6)*(eta(q^2)^2/(eta(q)*eta(q^4)))^4 in powers of q. - _G. C. Greubel_, Jan 25 2018
%F A112160 G.f.: exp(4*Sum_{k>=1} x^k/(k*(1 - (-x)^k))). - _Ilya Gutkovskiy_, Jun 07 2018
%e A112160 T24E = 1/q + 4*q^5 + 6*q^11 + 8*q^17 + 17*q^23 + 28*q^29 + 38*q^35 + ...
%t A112160 nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k+1))^4, {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Aug 27 2015 *)
%t A112160 eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/6)*(eta[q^2]^2/(eta[q]*eta[q^4]))^4, {q, 0, n}]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jan 25 2018 *)
%o A112160 (PARI) q='q+O('q^50); A = (eta(q^2)^2/(eta(q)*eta(q^4)))^4; Vec(A) \\ _G. C. Greubel_, Jul 01 2018
%K A112160 nonn
%O A112160 0,2
%A A112160 _Michael Somos_, Aug 28 2005