A094542 Denominator of Product_{k=0..n} ((2*k+1)/(2*k+2))^((-1)^t(k)) where t(k)=A010060(k) (Thue-Morse sequence).

2, 3, 5, 10, 9, 108, 216, 405, 765, 3825, 2550, 9775, 391, 10557, 102051, 204102, 198099, 7131564, 14263128, 69532749, 417196494, 815429511, 319081113, 3828973356, 7657946712, 7510678506, 7371591867, 58972734936, 57955963644

Offset

0,1

References

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

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

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 *)

Prog

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

Crossrefs

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

Sequence in context: A367297 A286144 A038807 * A175481 A288244 A246392

Adjacent sequences: A094539 A094540 A094541 * A094543 A094544 A094545

Keyword

frac,nonn

Author

Benoit Cloitre, May 08 2004

Status

approved