OFFSET
1,1
COMMENTS
Empirically, the infinite product converges slowly to 1.62816 ± 10^(-5).
LINKS
Gheorghe Coserea, Table of n, a(n) for n = 1..1000
Jean-Paul Allouche, Series and infinite products related to binary expansion of integers, December 07, 1992.
Jeffrey Shallit, Ten Problems I Can't Solve, talk for the University of Waterloo Pure Math Club, July 11 2000.
MATHEMATICA
Table[Numerator@ Product[(2 k/(2 k + 1))^((-1)^Plus @@ IntegerDigits[k, 2]), {k, 1, n}], {n, 22}] (* Michael De Vlieger, Aug 25 2015 *)
PROG
(PARI)
n = 22; R(k) = { if (hammingweight(k)%2, (2*k+1)/(2*k), (2*k)/(2*k+1)) };
p = vector(n); p[1] = R(1); for(i = 2, #p, p[i] = p[i-1] * R(i));
apply(numerator, p)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Gheorghe Coserea, Aug 24 2015
STATUS
approved