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A058088 McKay-Thompson series of class 8b for Monster.

%I A058088 #22 May 26 2024 12:53:00
%S A058088 1,8,-6,48,15,168,-26,496,51,1296,-102,3072,172,6840,-276,14448,453,
%T A058088 29184,-728,56880,1128,107472,-1698,197616,2539,354888,-3780,624048,
%U A058088 5505,1076736,-7882,1826416,11238,3050400,-15918,5022720,22259,8163152,-30810,13108224,42438,20814792,-58110
%N A058088 McKay-Thompson series of class 8b for Monster.
%H A058088 G. C. Greubel, <a href="/A058088/b058088.txt">Table of n, a(n) for n = 0..5000</a> (terms 0..999 from G. A. Edgar)
%H A058088 D. Alexander, C. Cummins, J. McKay and C. Simons, <a href="http://oeis.org/A007242/a007242_1.pdf">Completely Replicable Functions</a>, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.
%H A058088 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 A058088 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A058088 Expansion of q^(1/2)*(eta(q^2)^4*eta(q^4)^4 / (eta(q)^4*eta(q^8)^4) + 4*eta(q)^4*eta(q^8)^4 / (eta(q^2)^4*eta(q^4)^4)) in powers of q. - _G. A. Edgar_, Mar 23 2017
%e A058088 T8b = 1/q + 8*q - 6*q^3 + 48*q^5 + 15*q^7 + 168*q^9 - 26*q^11 + 496*q^13 + ...
%t A058088 eta[q_]:= q^(1/24)*QPochhammer[q]; F:= (eta[q^2]*eta[q^4]/(eta[q] *eta[q^8]))^4;  a:= CoefficientList[Series[q^(1/2)*(F + 4/F), {q,0,60}], q]; Table[a[[n]], {n,1,50}] (* _G. C. Greubel_, Jun 03 2018 *)
%o A058088 (PARI) q='q+O('q^30); F= (eta(q^2)*eta(q^4)/(eta(q)*eta(q^8)))^4; Vec(F + 4*q/F) \\ _G. C. Greubel_, Jun 03 2018
%Y A058088 Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y A058088 Agrees with A112145 except for signs.
%K A058088 sign
%O A058088 0,2
%A A058088 _N. J. A. Sloane_, Nov 27 2000
%E A058088 More terms from _G. A. Edgar_, Mar 23 2017