A094541 Numerator of Product_{k=0..n} ((2*k+1)/(2*k+2))^((-1)^t(k)) where t(k)=A010060(k) (Thue-Morse sequence).

1, 2, 4, 7, 7, 77, 143, 286, 572, 2717, 1729, 6916, 266, 7448, 74480, 144305, 144305, 5050675, 9835525, 49177625, 288040375, 576080750, 230432300, 2707579525, 5306855869, 5306855869, 5306855869, 41696724685, 41696724685, 492021351283

Offset

0,2

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, 29] // Numerator (* Jean-François Alcover, Jul 05 2011 *)

Prog

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

Crossrefs

Cf. A010060, A094542 (denominator), A261505, A261559.

Sequence in context: A370799 A063034 A351745 * A166928 A237199 A335192

Adjacent sequences: A094538 A094539 A094540 * A094542 A094543 A094544

Keyword

frac,nonn

Author

Benoit Cloitre, May 08 2004

Status

approved