%I #13 Jul 02 2018 22:41:02
%S 1,0,0,1,1,1,1,0,1,1,1,1,2,2,1,3,2,2,3,3,4,4,3,4,6,5,5,7,7,7,9,8,9,11,
%T 10,12,14,13,14,17,18,18,20,21,23,27,25,27,33,32,34,39,39,42,46,48,51,
%U 56,57,61,71,69,72,83,85,90,97,99,108,117,119,126,140,143,149,167,170
%N McKay-Thompson series of class 120a for the Monster group.
%H G. C. Greubel, <a href="/A112221/b112221.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 sqrt(T60B) in powers of q, where T60B = A058726. - _G. C. Greubel_, Jul 02 2018
%F a(n) ~ exp(sqrt(2*n/15)*Pi) / (2^(5/4) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018
%e T120a = 1/q +q^5 +q^7 +q^9 +q^11 +q^15 +q^17 +q^19 +q^21 +...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q^2]*eta[q^6] *eta[q^10]*eta[q^30])^2/(eta[q]*eta[q^3]*eta[q^4]*eta[q^5]*eta[q^12] *eta[q^15]*eta[q^20]*eta[q^60]); T60B := q*(B - 1);
%t a:= CoefficientList[Series[(T60B + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jul 02 2018 *)
%o (PARI) q='q+O('q^80); B = (eta(q^2)*eta(q^6)*eta(q^10)*eta(q^30))^2/ (q*eta(q)*eta(q^3)*eta(q^4)*eta(q^5)*eta(q^12)*eta(q^15)*eta(q^20) *eta(q^60)); Vec(sqrt(q*(B - 1))) \\ _G. C. Greubel_, Jul 02 2018
%K nonn
%O 0,13
%A _Michael Somos_, Aug 28 2005