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%I #16 Jul 02 2018 03:49:07
%S 1,0,1,1,1,0,2,1,3,3,3,2,6,4,6,6,8,6,11,9,13,14,16,14,24,19,27,27,33,
%T 30,43,38,51,51,61,58,79,72,92,94,110,106,138,130,160,164,189,188,235,
%U 226,270,279,321,320,388,381,448,462,525,530,631,626,724,750
%N McKay-Thompson series of class 78A for Monster.
%H G. C. Greubel, <a href="/A058754/b058754.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 David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&threadID=1602206&messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of B + 1 + 1/B, where B = eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/( eta(q^2)*eta(q^3)*eta(q^13)*eta(q^78)), in powers of q. - _G. C. Greubel_, Jun 30 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/39)) / (2^(3/4) * 39^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018
%e T78A = 1/q + q + q^2 + q^3 + 2*q^5 + q^6 + 3*q^7 + 3*q^8 + 3*q^9 + 2*q^10 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^6]*eta[q^26]* eta[q^39]/(eta[q^2]*eta[q^3]*eta[q^13]*eta[q^78]); a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 30 2018 *)
%o (PARI) q='q+O('q^50); B = eta(q)*eta(q^6)*eta(q^26)*eta(q^39)/(q*eta(q^2) *eta(q^3)*eta(q^13)*eta(q^78)); Vec(B + 1 + 1/B) \\ _G. C. Greubel_, Jun 30 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,7
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 24 2014
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