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%I #28 Jun 19 2018 12:33:26
%S 1,0,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64,76,89,104,122,
%T 141,164,191,220,254,293,336,385,442,504,575,656,745,846,960,1086,
%U 1228,1388,1564,1762,1984,2228,2501,2806,3142,3516,3932,4390,4898,5462,6082,6768,7527,8360,9280,10295,11408,12634,13984,15462
%N McKay-Thompson series of class 50a for Monster.
%C Apart from a(0) same as A034320. [_Joerg Arndt_, Apr 09 2016]
%H G. C. Greubel, <a href="/A058703/b058703.txt">Table of n, a(n) for n = -1..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 H. D. Nguyen, D. Taggart, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.391.2522&rep=rep1&type=pdf">Mining the OEIS: Ten Experimental Conjectures</a>, 2013; Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F G.f.: (E(q^2)*E(q^25))/(E(q)*E(q^50))/q - 1 where E(q) = prod(n>=1, 1 - q^n ). - _Joerg Arndt_, Apr 09 2016
%F a(n) ~ exp(2*Pi*sqrt(2*n)/5) / (2^(3/4) * sqrt(5) * n^(3/4)). - _Vaclav Kotesovec_, Sep 06 2017
%e T50a = 1/q + q + 2*q^2 + 2*q^3 + 3*q^4 + 4*q^5 + 5*q^6 + 6*q^7 + 8*q^8 + ...
%t nmax = 60; CoefficientList[Series[-x + Product[(1 + x^k)/(1 + x^(25*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 06 2017 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[-1 + (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 19 2018*)
%o (PARI) N=66; q='q+O('q^N); Vec( (eta(q^2)*eta(q^25))/(eta(q)*eta(q^50))/q - 1 ) \\ _Joerg Arndt_, Apr 09 2016
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Joerg Arndt_, Apr 09 2016
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