|
%I #13 Jun 29 2018 04:28:05
%S 1,-1,0,-1,1,-1,1,-1,2,-2,2,-3,4,-3,4,-5,6,-6,6,-8,9,-10,10,-12,14,
%T -15,16,-19,21,-22,24,-27,31,-34,36,-40,46,-48,52,-58,64,-69,74,-82,
%U 91,-98,104,-115,127,-136,145,-159,174,-186,200,-218,238,-254,272,-296,322,-343,366,-398,430,-460,492,-531
%N McKay-Thompson series of class 44b for the Monster group.
%H G. C. Greubel, <a href="/A112184/b112184.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 q^(1/2)*(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22))) in powers of q. - _G. C. Greubel_, Jun 28 2018
%F a(n) ~ (-1)^n * exp(sqrt(2*n/11)*Pi) / (2^(5/4) * 11^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2018
%e T44b = 1/q -q -q^5 +q^7 -q^9 +q^11 -q^13 +2*q^15 -2*q^17 +...
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]*eta[q^11]/(eta[q^2]*eta[q^22])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 28 2018 *)
%t nmax = 60; CoefficientList[Series[Product[(1 - x^(2*k-1))*(1 - x^(22*k-11)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 29 2018 *)
%o (PARI) q='q+O('q^50); Vec((eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))) \\ _G. C. Greubel_, Jun 28 2018
%K sign
%O 0,9
%A _Michael Somos_, Aug 28 2005
|
