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%I #21 Jun 20 2018 03:43:20
%S 1,0,3,3,3,6,7,6,12,16,18,24,33,33,48,57,69,87,106,117,153,181,207,
%T 258,307,345,429,496,570,681,805,906,1083,1252,1425,1671,1934,2190,
%U 2562,2929,3327,3840,4400,4953,5727,6500,7335,8388,9521,10686,12198,13775
%N McKay-Thompson series of class 42a for Monster.
%H G. C. Greubel, <a href="/A058675/b058675.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>, 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 a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, May 30 2018
%F Expansion of A - q/A, where A = q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))), in powers of q. - _G. C. Greubel_, Jun 19 2018
%e T42a = 1/q + 3*q^3 + 3*q^5 + 3*q^7 + 6*q^9 + 7*q^11 + 6*q^13 + 12*q^15 + ...
%t CoefficientList[Series[(QPochhammer[x^3]^2 * QPochhammer[x^7]^2 - x*QPochhammer[x]^2 * QPochhammer[x^21]^2) / (QPochhammer[x] * QPochhammer[x^3] * QPochhammer[x^7] * QPochhammer[x^21]), {x, 0, 100}], x] (* _Vaclav Kotesovec_, May 30 2018 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^7]/( eta[q]*eta[q^21])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 19 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^7)/(eta(q)* eta(q^21))); Vec(A - q/A) \\ _G. C. Greubel_, Jun 19 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Vaclav Kotesovec_, May 30 2018
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