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%I M5355 #31 May 11 2018 01:51:15
%S 1,0,79,352,1431,4160,13015,31968,81162,183680,412857,864320,1805030,
%T 3564864,7000753,13243392,24805035,45168896,81544240,143832672,
%U 251550676,432030080,735553575,1233715328,2052941733
%N McKay-Thompson series of class 6A for Monster.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vaclav Kotesovec, <a href="/A007254/b007254.txt">Table of n, a(n) for n = -1..1000</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%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 J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fischer_group_Fi22#Generalized_Monstrous_Moonshine">Generalized Monstrous Moonshine</a>
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F a(n) = A121665(n) + A226235(n) = A121666(n) + 64*A123653(n) = A121667(n) + 81*A284607(n) for n > 0. - _Seiichi Manyama_, Mar 30 2017
%F a(n) ~ exp(2*Pi*sqrt(2*n/3)) / (2^(3/4) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Mar 30 2017
%e T6A = 1/q + 79*q + 352*q^2 + 1431*q^3 + 4160*q^4 + 13015*q^5 + 31968*q^6 + ...
%t nmax = 50; Flatten[{1, 0, Rest[Rest[CoefficientList[Series[Product[((1 + x^k)/(1 + x^(3*k)))^12, {k, 1, nmax}] + x^2*Product[((1 + x^(3*k))/(1 + x^k))^12, {k, 1, nmax}], {x, 0, nmax}], x]]]}] (* _Vaclav Kotesovec_, Mar 30 2017 *)
%t eta[q_] := q^(1/24)*QPochhammer[q]; e6B:= (eta[q^2]*eta[q^3]/(eta[q]* eta[q^6]))^12; a:= CoefficientList[Series[q*(e6B - 12 + 1/e6B), {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (*_G. C. Greubel_, May 10 2018 *)
%o (PARI) q='q+O('q^50); F =(eta(q^2)*eta(q^3)/(eta(q)*eta(q^6)))^12/q; Vec(F -12 +1/F) \\ _G. C. Greubel_, May 10 2018
%Y Cf. A045484.
%K nonn
%O -1,3
%A _N. J. A. Sloane_
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