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%I #28 Jun 19 2018 12:33:32
%S 1,1,1,1,1,3,3,4,4,4,7,8,10,11,12,16,18,22,25,28,34,38,45,51,58,69,77,
%T 88,99,112,131,146,165,184,206,238,266,298,331,368,418,465,520,576,
%U 637,714,791,880,973,1074,1194,1316,1455,1604,1766,1954,2145,2360
%N McKay-Thompson series of class 60E for the Monster group.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A058729/b058729.txt">Table of n, a(n) for n = 0..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>, Comm. 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 Expansion of chi(-x^3) * chi(-x^15) / (chi(-x) * chi(-x^5)) in powers of x where chi() is a Ramanujan theta function. - _Michael Somos_, Jun 09 2012
%F G.f. is a period 1 Fourier series which satisfies f(-1 / (120 t)) = f(t) where q = exp(2 Pi i t). - _Michael Somos_, Jun 09 2012
%F Convolution square is A205962. - _Michael Somos_, Jun 09 2012
%F a(n) ~ exp(2*Pi*sqrt(n/15)) / (2 * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 06 2015
%F Expansion of q^(1/2)*eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15)/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30)) in powers of q. - _G. C. Greubel_, Jun 19 2018
%e 1 + x + x^2 + x^3 + x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 4*x^8 + 4*x^9 + 7*x^10 + ...
%e T60E = 1/q + q + q^3 + q^5 + q^7 + 3*q^9 + 3*q^11 + 4*q^13 + 4*q^15 + 4*q^17 + ...
%t nmax = 50; CoefficientList[Series[Product[(1 + x^k) * (1 + x^(5*k)) / ((1 + x^(3*k)) * (1 + x^(15*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 06 2015 *)
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)* eta[q^2]*eta[q^3]*eta[q^10]*eta[q^15]/(eta[q]* eta[q^5]*eta[q^6] *eta[q^30]), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 19 2018 *)
%o (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^3 + A) * eta(x^10 + A) * eta(x^15 + A) / (eta(x + A) * eta(x^5 + A) * eta(x^6 + A) * eta(x^30 + A)), n))} /* _Michael Somos_, Jun 09 2012 */
%Y Cf. A205962.
%K nonn
%O 0,6
%A _N. J. A. Sloane_, Nov 27 2000
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