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%I #26 Jun 01 2022 01:54:36
%S 1,2,79,352,1431,4160,13015,31968,81162,183680,412857,864320,1805030,
%T 3564864,7000753,13243392,24805035,45168896,81544240,143832672,
%U 251550676,432030080,735553575,1233715328,2052941733
%N McKay-Thompson series of class 6A for Monster.
%D J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%D D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
%D J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.
%H Seiichi Manyama, <a href="/A045484/b045484.txt">Table of n, a(n) for n = -1..10000</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
%t eta[q_]:= q^(1/24)*QPochhammer[q]; h:= (eta[q]*eta[q^6]/(eta[q^2]* eta[q^3]))^12; g := h - 10 + 1/h; A045484 := CoefficientList[Series[q*g, {q, 0, 60}], q]; Table[A045484[[n]], {n, 1, 50}] (* _G. C. Greubel_, May 28 2018 *)
%o (PARI) q='q+O('q^30); {h =q*(eta(q)*eta(q^6)/(eta(q^2)*eta(q^3)))^12}; Vec(h - 10 + 1/h) \\ _G. C. Greubel_, May 28 2018
%Y Cf. A007254, A121665, A121666, A121667.
%K nonn
%O -1,2
%A _N. J. A. Sloane_
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