A112224 - OEIS

%I #12 Jul 03 2018 14:57:09

%S 1,1,0,0,1,0,1,0,1,0,1,1,1,1,2,1,2,1,2,2,3,2,3,2,4,3,4,3,5,4,5,5,6,5,

%T 8,6,9,6,9,8,11,10,12,11,14,12,16,13,18,16,20,18,22,20,25,23,29,25,31,

%U 29,36,33,39,36,45,40,49,45,54,51,61,58,66,63,75,70,84,77,91,86,101

%N McKay-Thompson series of class 140a for the Monster group.

%H G. C. Greubel, <a href="/A112224/b112224.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(T70A + 2) in powers of q, where T70A = A058744. - _G. C. Greubel_, Jul 03 2018

%F a(n) ~ exp(2*Pi*sqrt(n/35)) / (2 * 35^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 03 2018

%e T140a = 1/q +q +q^7 +q^11 +q^15 +q^19 +q^21 +q^23 +q^25 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 130; b:= eta[q]*eta[q^10]* eta[q^14]*eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); T70A:= 1 + b + 1/b; a:= CoefficientList[Series[(q*T70A + 2*q + O[q]^nmax)^(1/2), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 80}] (* _G. C. Greubel_, Jul 03 2018 *)

%o (PARI) q='q+O('q^80); 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)); T70A = b + 1 + 1/b; Vec(sqrt(q*( T70A + 2))) \\ _G. C. Greubel_, Jul 03 2018

%K nonn

%O 0,15

%A _Michael Somos_, Aug 28 2005