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%I #16 Jun 30 2018 16:58:19
%S 1,0,1,0,2,2,2,2,3,2,4,4,7,4,10,8,11,10,14,14,21,18,25,22,33,32,41,38,
%T 52,50,65,62,82,78,101,102,124,122,150,152,189,186,230,226,279,280,
%U 334,340,402,412,487,492,582,592,697,714,831,850,980,1014,1173
%N McKay-Thompson series of class 70A for Monster.
%H G. C. Greubel, <a href="/A058744/b058744.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^10)*eta(q^14)*eta(q^35)/ (eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)), in powers of q. - _G. C. Greubel_, Jun 30 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/35)) / (2^(3/4) * 35^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 30 2018
%e T70A = 1/q + q + 2*q^3 + 2*q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 2*q^8 + 4*q^9 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[1 + B + 1/B, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 30 2018 *)
%o (PARI) q='q+O('q^50); B = eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/ (q*eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(B + 1 + 1/B) \\ _G. C. Greubel_, Jun 30 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,5
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 24 2014
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