A112200 - OEIS

%I #16 Jul 02 2018 20:25:41

%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,

%T 7,-7,9,-8,9,-11,10,-12,14,-13,14,-17,18,-18,20,-21,23,-27,25,-27,33,

%U -32,34,-39,39,-42,46,-48,51,-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 60a for the Monster group.

%H G. C. Greubel, <a href="/A112200/b112200.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(T30C), where T30C = A058614, in powers of q. - _G. C. Greubel_, Jun 28 2018

%F a(n) ~ (-1)^n * exp(sqrt(2*n/15)*Pi) / (2^(5/4) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T60a = 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; A:= eta[q]*eta[q^3] *eta[q^5]*eta[q^15]/(eta[q^2]*eta[q^6]*eta[q^10]*eta[q^30]); a:= CoefficientList[Series[(q*(1 + A) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 28 2018 *)

%o (PARI) q='q+O('q^70); A = eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/(q*eta(q^2) *eta(q^6)*eta(q^10)*eta(q^30)); Vec(sqrt(q*(1 + A))) \\ _G. C. Greubel_, Jul 02 2018

%K sign

%O 0,13

%A _Michael Somos_, Aug 28 2005