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%I #13 Apr 05 2017 14:43:16
%S 1,-2,-3,6,2,2,-5,-16,12,2,17,-10,-48,56,10,24,-35,-126,106,14,94,-70,
%T -284,296,60,152,-175,-620,536,80,398,-320,-1243,1218,216,652,-680,
%U -2422,2122,328,1435,-1190,-4470,4240,734,2312,-2285,-8120,7130,1112,4549,-3850,-14178,13132,2210
%N Expansion of (eta(q) * eta(q^2) / (eta(q^5) * eta(q^10)))^2 in powers of q.
%C A058099(n) = a(n) unless n=0.
%C McKay-Thompson series of class 10C for Monster with a(0)=-2.
%H Seiichi Manyama, <a href="/A132041/b132041.txt">Table of n, a(n) for n = -1..10000</a>
%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 Euler transform of period 10 sequence [ -2, -4, -2, -4, 0, -4, -2, -4, -2, 0, ...].
%F G.f. is a period 1 Fourier series which satisfies f(-1 / (10 t)) = 25 / f(t) where q = exp(2 Pi i t).
%F G.f.: (Product_{k>0} (1-x^k)* (1-x^(2k))/( (1-x^(5k))* (1-x^(10k))))^2.
%e G.f. = 1/q - 2 - 3*q + 6*q^2 + 2*q^3 + 2*q^4 - 5*q^5 - 16*q^6 + 12*q^7 + ...
%t a[ n_] := SeriesCoefficient[ 1/q (QPochhammer[ q] QPochhammer[ q^2] / (QPochhammer[ q^5] QPochhammer[ q^10]))^2, {q, 0, n}]; (* _Michael Somos_, Aug 26 2015 *)
%o (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^2 + A) / (eta(x^5 + A) * eta(x^10 + A)))^2, n))};
%K sign
%O -1,2
%A _Michael Somos_, Aug 07 2007
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