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A112143 McKay-Thompson series of class 8D for the Monster group.

%I A112143 #26 May 11 2018 06:17:03
%S A112143 1,-4,2,8,-1,-20,-2,40,3,-72,2,128,-4,-220,-4,360,5,-576,8,904,-8,
%T A112143 -1384,-10,2088,11,-3108,12,4552,-15,-6592,-18,9448,22,-13392,26,
%U A112143 18816,-29,-26216,-34,36224,38,-49700,42,67728,-51,-91688,-56,123392,66,-165128,78,219784,-85,-291072
%N A112143 McKay-Thompson series of class 8D for the Monster group.
%C A112143 The convolution square of this sequence is A007248, except for the constant term: T8D(q)^2 = T4C(q^2) - 8. - _G. A. Edgar_, Apr 02 2017
%H A112143 Seiichi Manyama, <a href="/A112143/b112143.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..499 from G. A. Edgar)
%H A112143 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 A112143 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 A112143 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F A112143 Expansion of q^(1/2)*(eta(q) / eta(q^4))^4 in powers of q. - _G. A. Edgar_, Apr 02 2017
%F A112143 a(0) = 1, a(n) = -(4/n)*Sum_{k=1..n} A046897(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Apr 28 2017
%e A112143 T8D = 1/q -4*q +2*q^3 +8*q^5 -q^7 -20*q^9 -2*q^11 +40*q^13 +...
%t A112143 eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q]/eta[q^4])^4, {q, 0, 50}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, May 10 2018 *)
%o A112143 (PARI) q='q+O('q^50); Vec((eta(q)/eta(q^4))^4) \\ _G. C. Greubel_, May 10 2018
%Y A112143 Cf. A007248, A046897.
%K A112143 sign
%O A112143 0,2
%A A112143 _Michael Somos_, Aug 28 2005