A112145 - OEIS

%I #22 Jun 06 2018 18:31:34

%S 1,-8,-6,-48,15,-168,-26,-496,51,-1296,-102,-3072,172,-6840,-276,

%T -14448,453,-29184,-728,-56880,1128,-107472,-1698,-197616,2539,

%U -354888,-3780,-624048,5505,-1076736,-7882,-1826416,11238,-3050400,-15918,-5022720,22259,-8163152,-30810

%N McKay-Thompson series of class 8c for the Monster group.

%C This sequence agrees with A058088 except for alternating signs: T8c(q) = i*T8b(i*q). - _G. A. Edgar_, Mar 25 2017

%H G. C. Greubel, <a href="/A112145/b112145.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..503 from G. A. Edgar)

%H 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 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 q^(1/2)*(eta(q^4)^8*eta(q)^4 / (eta(q^2)^8*eta(q^8)^4) - 4*eta(q^2)^8*eta(q^8)^4 / (eta(q)^4*eta(q^4)^8)) in powers of q. - _G. A. Edgar_, Mar 25 2017

%e T8c = 1/q -8*q -6*q^3 -48*q^5 +15*q^7 -168*q^9 -26*q^11 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/2)*(eta[q^4]^8*eta[q]^4/(eta[q^2]^8*eta[q^8]^4) - 4*eta[q^2]^8 *eta[q^8]^4 /(eta[q]^4*eta[q^4]^8)), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jan 23 2018 *)

%o (PARI) q='q+O('q^30); F= eta(q^4)^8*eta(q)^4/(eta(q^2)^8*eta(q^8)^4) - 4*q*eta(q^2)^8*eta(q^8)^4/(eta(q)^4* eta(q^4)^8); Vec(F) \\ _G. C. Greubel_, Jun 06 2018

%Y Cf. A058088.

%K sign

%O 0,2

%A _Michael Somos_, Aug 28 2005