A112170 - OEIS

%I #15 Jul 03 2018 03:57:57

%S 1,1,1,0,-2,2,0,1,0,-1,2,1,3,0,-2,5,2,3,0,-5,7,3,4,0,-5,9,3,7,0,-7,14,

%T 8,11,0,-14,21,7,13,0,-14,26,11,20,0,-21,39,16,26,0,-32,51,20,34,0,

%U -38,65,25,47,0,-49,90,40,63,0,-74,118,44,77,0,-85,146,60,105,0,-111,196,80,132,0,-152

%N McKay-Thompson series of class 30f for the Monster group.

%H G. C. Greubel, <a href="/A112170/b112170.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(2 + T15b), in powers of q, where T15b = A058513. - _G. C. Greubel_, Jun 30 2018

%e T30f = 1/q + q + q^3 - 2*q^7 + 2*q^9 + q^13 - q^17 + 2*q^19 + q^21 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; B:= (eta[q]/eta[q^25]);

%t d:= q*(eta[q^3]/eta[q^15])^2; c:= (eta[q^3]*eta[q^5]/(eta[q]* eta[q^15]))^3; T25A := B + 5/B; A:= (eta[q^3]/eta[q^75]); T15b:= 2 + (-5 + T25A*(A + 5/A))*(-B + A)*(1/(A*B))^2*(d^3/c)/q^3; a:= CoefficientList[ Series[(q*(T15b + 2) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* _G. C. Greubel_, Jun 30 2018, fixed by _Vaclav Kotesovec_, Jul 03 2018 *)

%K sign

%O 0,5

%A _Michael Somos_, Aug 28 2005