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A261559
Denominator of Product_{k=1..n} (2k/(2k+1))^((-1)^A000120(k)).
4
2, 8, 28, 224, 1232, 4004, 56056, 896896, 8520512, 14910896, 328039712, 41004964, 1066129064, 29851613792, 462700013776, 1346036403712, 4711127412992, 43577928570176, 127381637358976, 652830891464752, 9139632480506528, 402143829142287232, 9450379984843749952
OFFSET
1,1
COMMENTS
For all n, a(n) is even, 2-adic valuation of a(2^n) is 2n+1 and 2-adic valuation of a(3*2^n) is 2.
LINKS
Jeffrey Shallit, Ten Problems I Can't Solve, talk for the University of Waterloo Pure Math Club, July 11 2000.
MATHEMATICA
Table[Denominator@ Product[(2 k/(2 k + 1))^((-1)^DigitCount[k, 2, 1]), {k, 1, n}], {n, 23}] (* Michael De Vlieger, Aug 26 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(denominator, p)
CROSSREFS
Cf. A000120, A010060, A094541, A094542, A261505 (numerator).
Sequence in context: A225689 A330211 A216785 * A061230 A241627 A293169
KEYWORD
nonn,frac
AUTHOR
Gheorghe Coserea, Aug 24 2015
STATUS
approved