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%I #14 Jun 29 2018 04:44:52
%S 1,-1,1,0,1,-2,2,-2,3,-4,4,-4,5,-7,7,-8,10,-12,14,-14,17,-20,22,-24,
%T 28,-33,36,-40,45,-52,56,-62,71,-80,88,-96,109,-122,133,-144,163,-182,
%U 198,-216,240,-268,290,-316,349,-386,420,-456,502,-552,600,-650,713,-780,846,-916,1001,-1093,1182
%N McKay-Thompson series of class 36f for the Monster group.
%H G. C. Greubel, <a href="/A112176/b112176.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 q^(1/2)*(eta(q)*eta(q^6)^4*eta(q^9)/(eta(q^2)*eta(q^3)* eta(q^18))^2) in powers of q. - _G. C. Greubel_, Jun 19 2018
%F a(n) ~ (-1)^n * exp(Pi*sqrt(2*n)/3) / (2^(5/4)*sqrt(3)*n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T36f = 1/q - q + q^3 + q^7 - 2*q^9 + 2*q^11 - 2*q^13 + 3*q^15 - 4*q^17 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= SeriesCoefficient[q^(1/2)*(eta[q] *eta[q^6]^4*eta[q^9]/(eta[q^2]*eta[q^3]*eta[q^18])^2), {q, 0, n}]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 19 2018 *)
%o (PARI) q='q+O('q^50); Vec((eta(q)*eta(q^6)^4*eta(q^9)/(eta(q^2)*eta(q^3)* eta(q^18))^2)) \\ _G. C. Greubel_, Jun 19 2018
%K sign
%O 0,6
%A _Michael Somos_, Aug 28 2005
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