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A094541 Numerator of prod(k=0..n, ((2*k+1)/(2*k+2))^((-1)^t(k)) ) where t(k)=A010060(k) (Thue-Morse sequence). 5
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 (list; graph; refs; listen; history; text; internal format)
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

prod(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-Fran├žois 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: A178183 A010759 A063034 * A166928 A237199 A335192

Adjacent sequences:  A094538 A094539 A094540 * A094542 A094543 A094544

KEYWORD

frac,nonn

AUTHOR

Benoit Cloitre, May 08 2004

STATUS

approved

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Last modified July 11 23:53 EDT 2020. Contains 335654 sequences. (Running on oeis4.)