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%I #23 Jul 20 2022 05:15:34
%S 1,1,0,2,1,2,1,2,3,4,5,5,5,7,8,11,10,13,14,16,19,22,23,28,32,37,38,45,
%T 51,58,65,73,78,91,98,114,123,136,153,170,187,206,226,255,276,312,334,
%U 369,406,448,492,538,586,646,701,773,837,917,997,1093,1188,1291,1397,1532,1657,1808
%N McKay-Thompson series of class 70a for Monster.
%H G. C. Greubel, <a href="/A058746/b058746.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>, 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 sqrt(2 + T35A) in powers of q, where T35A = A058640. - _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_, Jul 02 2018
%e T70a = 1/q + q + 2*q^5 + q^7 + 2*q^9 + q^11 + 2*q^13 + 3*q^15 + 4*q^17 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 80; B:= eta[q^5]*eta[q^7]/( eta[q]*eta[q^35]); a:= CoefficientList[Series[(q (1 + B - 1/B + O[q]^nmax))^(1/2), {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^5)*eta(q^7)/(q*eta(q)*eta(q^35)); Vec(sqrt(q*(B + 1 - 1/B))) \\ _G. C. Greubel_, Jul 01 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jun 30 2018
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