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%I #37 Aug 22 2021 13:45:26
%S 1,1,2,2,4,4,6,7,11,12,16,19,25,29,37,44,56,65,80,94,114,133,160,187,
%T 223,258,305,353,415,478,560,643,749,857,993,1134,1308,1490,1712,1946,
%U 2227,2525,2880,3259,3706,4186,4747,5350,6050,6806,7677,8620,9702,10875,12212,13664,15315,17107,19136,21342,23834,26540,29585,32896,36613
%N McKay-Thompson series of class 45b for Monster.
%H Seiichi Manyama, <a href="/A058686/b058686.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^9)*E(q^15))/(E(q^3)*E(q^45))/q where E(q) = Product_{n>=1} (1 - q^n), note that only every third term is nonzero and the zeros are omitted in this sequence, cf. the PARI/GP program. - _Joerg Arndt_, Apr 09 2016
%F a(n) ~ exp(4*Pi*sqrt(n/5)/3) / (5^(1/4)*sqrt(6)*n^(3/4)). - _Vaclav Kotesovec_, Apr 09 2016
%F Expansion of q^(1/3)*(eta(q^3)*eta(q^5)/(eta(q)*eta(q^15))) in powers of q. - _G. C. Greubel_, Jun 06 2018
%e T45b = 1/q + q^2 + 2*q^5 + 2*q^8 + 4*q^11 + 4*q^14 + 6*q^17 + 7*q^20 + ...
%t nmax = 50; CoefficientList[Series[Product[(1-x^(3*k))*(1-x^(5*k))/((1-x^k)*(1-x^(15*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^(1/3)*(eta[q^3]*eta[q^5]/(eta[q]*eta[q^15])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 06 2018 *)
%o (PARI) { N=66; q='q+O('q^N); my(E=eta); Vec( (E(q^3)*E(q^5))/(E(q^1)*E(q^15))/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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