A261559 Denominator of Product_{k=1..n} (2k/(2k+1))^((-1)^A000120(k)).

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

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[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

Adjacent sequences: A261556 A261557 A261558 * A261560 A261561 A261562

Keyword

nonn,frac

Author

Gheorghe Coserea, Aug 24 2015

Status

approved