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%I #36 Aug 22 2021 13:44:44
%S 1,1,3,2,7,6,12,10,21,22,36,36,59,63,93,98,142,156,218,238,327,358,
%T 482,528,696,769,996,1106,1411,1572,1978,2206,2745,3068,3776,4224,
%U 5161,5778,6999,7832,9429,10554,12612,14112,16776,18782,22190,24828,29195,32666,38220,42730,49794,55656,64598,72146,83439,93134,107346
%N McKay-Thompson series of class 36C for Monster.
%H G. C. Greubel, <a href="/A058646/b058646.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 G.f.: (E(q^6)*E(q^12))^2/(E(q^2)*E(q^4)*E(q^18)*E(q^36))/q where E(q) = prod(n>=1, 1 - q^n ), note that every second term is zero and has been omitted from this sequence, cf. the PARI/GP program. - _Joerg Arndt_, Apr 09 2016
%F a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*sqrt(3)*n^(3/4)). - _Vaclav Kotesovec_, Sep 10 2015
%e T36C = 1/q + q + 3*q^3 + 2*q^5 + 7*q^7 + 6*q^9 + 12*q^11 + 10*q^13 + ...
%t nmax = 50; CoefficientList[Series[Product[((1-x^(3*k)) * (1-x^(6*k)))^2 / ((1-x^k) * (1-x^(2*k)) * (1-x^(9*k)) * (1-x^(18*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 10 2015 *)
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^3]*eta[q^6])^2/(eta[q]*eta[q^2]*eta[q^9]*eta[q^18]), {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); my(E=eta); Vec( (E(q^3)*E(q^6))^2 / (E(q^1)*E(q^2)*E(q^9)*E(q^18))/q ) } \\ _Joerg Arndt_, Apr 09 2016
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Nov 27 2000
%E Offset corrected by _N. J. A. Sloane_, Feb 17 2014
%E More terms from _Vaclav Kotesovec_, Sep 10 2015
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