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A058664 McKay-Thompson series of class 40C for Monster. 2

%I #32 Aug 22 2021 13:45:05

%S 1,1,2,3,4,5,8,10,13,18,22,28,36,45,56,70,85,104,128,154,187,226,270,

%T 323,386,457,542,642,755,888,1042,1218,1422,1658,1926,2236,2591,2994,

%U 3456,3984,4583,5265,6042,6918,7914,9042,10314,11752,13376,15202,17258,19574,22170,25088,28362,32026,36129,40722,45850

%N McKay-Thompson series of class 40C for Monster.

%C Also McKay-Thompson series of class 40D for Monster.

%H Seiichi Manyama, <a href="/A058664/b058664.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>, Commun. 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 G.f.: (E(q^8)*E(q^10))/(E(q^2)*E(q^40))/q where E(q) = prod(n>=1, 1 - q^n ), note that every second terms is zero and is omitted in this sequence, cf. the PARI/GP program. - _Joerg Arndt_, Apr 09 2016

%F a(n) ~ exp(sqrt(2*n/5)*Pi) / (2^(5/4)*5^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Apr 09 2016

%e T40C = 1/q + q + 2*q^3 + 3*q^5 + 4*q^7 + 5*q^9 + 8*q^11 + 10*q^13 + 13*q^15 + ...

%t nmax = 50; CoefficientList[Series[Product[(1-x^(4*k))*(1-x^(5*k))/((1-x^k)*(1-x^(20*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Apr 09 2016 *)

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*( eta[q^4]*eta[q^5]/(eta[q]*eta[q^20])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 14 2018 *)

%o (PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^4)*E(q^5))/(E(q^1)*E(q^20))/q ) } \\ _Joerg Arndt_, Apr 09 2016

%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 _Joerg Arndt_, Apr 09 2016

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