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Denominator of Product_{k=0..n} ((2*k+1)/(2*k+2))^((-1)^t(k)) where t(k)=A010060(k) (Thue-Morse sequence).
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%I #21 Jan 09 2021 09:57:04

%S 2,3,5,10,9,108,216,405,765,3825,2550,9775,391,10557,102051,204102,

%T 198099,7131564,14263128,69532749,417196494,815429511,319081113,

%U 3828973356,7657946712,7510678506,7371591867,58972734936,57955963644

%N Denominator of Product_{k=0..n} ((2*k+1)/(2*k+2))^((-1)^t(k)) where t(k)=A010060(k) (Thue-Morse sequence).

%D J.-P. Allouche and J. Shallit, Automatic sequences, Cambridge, pp. 153, 207

%H Gheorghe Coserea, <a href="/A094542/b094542.txt">Table of n, a(n) for n = 0..1000</a>

%F Product_{k>=0} ((2*k+1)/(2*k+2))^((-1)^t(k)) = 1/sqrt(2).

%t t[0] = 0; t[1] = 1; t[n_?EvenQ] := t[n] = t[n/2]; t[n_?OddQ] := t[n] = 1 - t[(n-1)/2]; a[n_] = Product[((2k + 1)/(2k + 2))^((-1)^t[k]), {k, 0, n}]; a /@ Range[0, 28] // Denominator (* _Jean-François Alcover_, Jul 05 2011 *)

%o (PARI) a(n)=denominator(prod(k=0,n,((2*k+1)/(2*k+2))^((-1)^(subst(Pol(binary(k)),x,1)%2))))

%Y Cf. A010060, A094541 (numerator), A261505, A261559.

%K frac,nonn

%O 0,1

%A _Benoit Cloitre_, May 08 2004