A112218 - OEIS

%I #13 Jul 02 2018 20:26:23

%S 1,1,0,1,0,1,1,1,1,2,1,2,3,2,2,4,3,4,5,5,5,7,6,7,9,9,9,12,11,13,15,15,

%T 16,20,19,22,25,26,27,33,32,36,41,42,44,52,52,57,64,66,70,81,82,89,99,

%U 103,109,123,125,136,150,156,165,185,189,204,223,233,247,273,281,302

%N McKay-Thompson series of class 102a for the Monster group.

%H G. C. Greubel, <a href="/A112218/b112218.txt">Table of n, a(n) for n = 0..2500</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(2 + T51A) in powers of q, where T51A = A058704. - _G. C. Greubel_, Jul 02 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/51)) / (2^(3/4) * 51^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018

%e T102a = 1/q +q +q^5 +q^9 +q^11 +q^13 +q^15 +2*q^17 +q^19 +...

%t QP := QPochhammer; nmax = 100; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; A := G[x^17]*G[x^3] + x^4*H[x^17]*H[x^3]; B := G[x^51]*H[x] - x^10*H[x^51]*G[x]; T51A := (A*B)/x; a:= CoefficientList[ Series[(x*(2 + T51A) + O[x]^nmax)^(1/2), {x, 0, nmax}], x]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jul 02 2018 *)

%K nonn

%O 0,10

%A _Michael Somos_, Aug 28 2005