A058496 - OEIS

%I #27 Feb 19 2018 03:22:48

%S 1,0,-1,2,1,2,-2,0,-2,-2,1,0,0,4,-1,-4,6,2,4,-6,-2,-4,-4,0,-1,0,11,-2,

%T -11,16,6,12,-14,-2,-12,-12,3,-2,-2,24,-5,-24,34,12,25,-32,-6,-24,-22,

%U 4,-3,-2,51,-10,-50,72,27,52,-64,-12,-50,-48,10,-8,-4,98

%N McKay-Thompson series of class 13B for the Monster group.

%H G. C. Greubel, <a href="/A058496/b058496.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>, Commun. 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 2 + ( eta(q) / eta(q^13) )^2 in powers of q. - _Michael Somos_, Jul 05 2012

%F G.f.: 2 + (1/x) * Product_{k>0} ((1 - x^k) / (1 - x^(13*k)))^2. - _Michael Somos_, Jul 05 2012

%F a(n) = A133099(n) unless n=0. - _Michael Somos_, Jul 05 2012

%e T13B = 1/q - q + 2*q^2 + q^3 + 2*q^4 - 2*q^5 - 2*q^7 - 2*q^8 + q^9 + 4*q^12 - ...

%t QP = QPochhammer; s = 2*q+(QP[q]/QP[q^13])^2+O[q]^70; CoefficientList[s, q] (* _Jean-François Alcover_, Nov 13 2015, adapted from PARI *)

%t eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[2 + (eta[q] /eta[q^13])^2, {q, 0, n}]; Table[a[n], {n,-1,50}] (* _G. C. Greubel_, Feb 18 2018 *)

%o (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x*O(x^n); polcoeff( (eta(x + A) / eta(x^13 + A))^2 + 2*x, n))} /* _Michael Somos_, Jul 05 2012 */

%Y Cf. A000521, A007240, A007241, A007267, A014708, A045478.

%Y Cf. A133099.

%K sign

%O -1,4

%A _N. J. A. Sloane_, Nov 27 2000