A112223 - OEIS

%I #12 Jul 03 2018 17:44:54

%S 1,0,1,0,0,1,1,0,1,1,1,1,2,1,2,1,2,2,3,1,3,2,3,3,5,3,5,4,5,5,7,5,8,7,

%T 8,8,11,8,12,10,12,12,16,12,18,16,19,18,23,19,26,23,27,27,33,28,37,34,

%U 39,38,47,41,52,48,55,55,66,58,73,68,77,77,91,82,100,95,107,107,124

%N McKay-Thompson series of class 132a for the Monster group.

%H G. C. Greubel, <a href="/A112223/b112223.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(T66A) in powers of q, where T66A = A058739. - _G. C. Greubel_, Jul 03 2018

%F a(n) ~ exp(2*Pi*sqrt(n/33)) / (2 * 33^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 03 2018

%e T132a = 1/q +q^3 +q^9 +q^11 +q^15 +q^17 +q^19 +q^21 +2*q^23 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 120; b:= (eta[q^2]*eta[q^3]* eta[q^22]*eta[q^33])/(eta[q]*eta[q^6]*eta[q^11]*eta[q^66]);  T66A:= -1 + b + 1/b; a:= CoefficientList[Series[(q*T66A + 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^2)*eta(q^3)* eta(q^22)*eta(q^33))/(q* eta(q)*eta(q^6)*eta(q^11)*eta(q^66)); T66A = b - 1 + 1/b; Vec(sqrt(q*T66A)) \\ _G. C. Greubel_, Jul 03 2018

%K nonn

%O 0,13

%A _Michael Somos_, Aug 28 2005