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%I #13 Jul 02 2018 16:35:56
%S 1,2,0,0,4,4,0,0,2,-2,0,0,-8,-4,0,0,-4,0,0,0,8,-8,0,0,-8,-2,0,0,-16,4,
%T 0,0,6,-8,0,0,12,4,0,0,8,8,0,0,-8,4,0,0,-8,2,0,0,24,-4,0,0,0,8,0,0,
%U -16,4,0,0,12,8,0,0,16,0,0,0,10,-8,0,0,-24,0,0,0,-8,-6,0,0,16,8,0,0,-24,-8,0,0,-16,-8,0,0,8,0,0
%N Euler transform of period-16 sequence [2,-3,2,1,2,-3,2,-6,2,-3,2,1,2,-3,2,-3,...].
%H Alois P. Heinz, <a href="/A080964/b080964.txt">Table of n, a(n) for n = 0..20000</a> (1501 terms from G. C. Greubel)
%F a(4*n+2) = a(4*n+3) = 0.
%F a(n) = 2*A072071(n) - A072070(n).
%F a(4*n) = A080965(n).
%F a(4*n+1) = 2*A080966(n).
%F Expansion of eta(q^2)^5*eta(q^8)^7/(eta(q)^2*eta(q^4)^4*eta(q^16)^3) in powers of q. - _G. C. Greubel_, Jul 02 2018
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[eta[q^2]^5 *eta[q^8]^7/(eta[q]^2*eta[q^4]^4*eta[q^16]^3), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 70}] (* _G. C. Greubel_, Jul 02 2018 *)
%o (PARI) a(n)=local(X); if(n<0,0,X=x+x*O(x^n); polcoeff(eta(X)^-2*eta(X^2)^5*eta(X^4)^-4*eta(X^8)^7*eta(X^16)^-3,n))
%K sign
%O 0,2
%A _Michael Somos_, Feb 28 2003
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