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A058492 McKay-Thompson series of class 12d for Monster.

%I A058492 #27 Jun 04 2018 09:23:24
%S A058492 1,-3,3,-7,18,-21,30,-57,75,-104,156,-207,293,-411,525,-712,984,-1248,
%T A058492 1622,-2169,2757,-3530,4560,-5736,7284,-9249,11472,-14374,18078,
%U A058492 -22242,27484,-34140,41787,-51184,62796,-76317,92893,-112998,136275,-164671,199014
%N A058492 McKay-Thompson series of class 12d for Monster.
%C A058492 The convolution square of this sequence is A121666: T12d(q)^2 = T6C(q^2). - _G. A. Edgar_, Apr 15 2017
%H A058492 G. C. Greubel, <a href="/A058492/b058492.txt">Table of n, a(n) for n = 0..2500</a> (terms 0..502 from G. A. Edgar)
%H A058492 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 A058492 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A058492 a(n) ~ (-1)^n * exp(Pi*sqrt(2*n/3)) / (2^(5/4)*3^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Nov 07 2015
%F A058492 Expansion of q^(1/2) * (eta(q)^3*eta(q^3)^3 / (eta(q^2)^3*eta(q^6)^3)) in powers of q. - _G. A. Edgar_, Apr 15 2017
%e A058492 T12d = 1/q - 3*q + 3*q^3 - 7*q^5 + 18*q^7 - 21*q^9 + 30*q^11 - 57*q^13 + ...
%t A058492 nmax = 60; CoefficientList[Series[Product[((1 - x^(2*k-1)) * (1 - x^(6*k-3)))^3, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 07 2015 *)
%t A058492 eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^3]/(eta[q^2]*eta[q^6]))^3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 03 2018 *)
%o A058492 (PARI) { my(q='q+O('q^66)); Vec( (eta(q)^3*eta(q^3)^3 / (eta(q^2)^3*eta(q^6)^3)) ) } \\ _Joerg Arndt_, Apr 16 2017
%Y A058492 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K A058492 sign
%O A058492 0,2
%A A058492 _N. J. A. Sloane_, Nov 27 2000
%E A058492 More terms from _Vaclav Kotesovec_, Nov 07 2015