A261505 Numerator of Product_{k=1..n} (2k/(2k+1))^((-1)^A000120(k)).

3, 15, 45, 405, 2025, 6075, 91125, 1549125, 13942125, 23236875, 534448125, 64133775, 1731611925, 50216745825, 753251187375, 2259753562125, 7683162111225, 69148459001025, 207445377003075, 1037226885015375, 14866918685220375, 669011340834916875

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

Cf. A000120, A010060, A094541, A094542, A261559 (denominator).

Sequence in context: A100737 A178669 A110464 * A331505 A088108 A226030

Adjacent sequences: A261502 A261503 A261504 * A261506 A261507 A261508

Keyword

nonn,frac

Author

Gheorghe Coserea, Aug 24 2015

Status

approved