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
KEYWORD
frac,nonn
AUTHOR
Benoit Cloitre, May 08 2004
STATUS
approved