A046879 Denominator of (1/n)*Sum_{k=0..n-1} 1/binomial(n-1,k) for n>0 else 1.

1, 1, 1, 6, 3, 15, 30, 420, 105, 315, 315, 6930, 3465, 90090, 180180, 72072, 9009, 153153, 153153, 5819814, 14549535, 14549535, 29099070, 1338557220, 334639305, 1673196525, 1673196525, 10039179150, 10039179150, 582272390700, 1164544781400

Offset

0,4

Comments

For n>=1 a(n) is the denominator of (1/2^n)*Sum_{k=1..n} 2^k/k. - Groux Roland, Jan 13 2009

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000 (terms 0..200 from T. D. Noe)

Eric Weisstein's World of Mathematics, Leibniz Harmonic Triangle

Formula

a(n) = denominator((-1)^(n-1)/(n-1)!*Sum_{k=0..n-1} 2^k*bern(k) * stirling1(n-1,k)), n>0, a(0)=1. - Vladimir Kruchinin, Nov 20 2015

a(n) = denominator(-2*LerchPhi(2,1,n+1)-i*Pi/2^n). - Peter Luschny, Nov 20 2015

Maple

a := n -> -2*LerchPhi(2, 1, n+1)-I*Pi/2^n:
seq(denom(simplify(a(n))), n=0..30); # Peter Luschny, Nov 20 2015

Mathematica

Denominator[Simplify[-2*LerchPhi[2, 1, # + 1] - I*Pi/2^#]] & /@
Range[0, 100] (* Julien Kluge, Jul 21 2016 *)

Prog

(Maxima)
a(n):=if n=0 then 1 else denom((-1)^(n-1)/(n-1)!*sum(2^k*bern(k)*(stirling1(n-1, k)), k, 0, n-1)); /* Vladimir Kruchinin, Nov 20 2015 */
(PARI) vector(30, n, n--; denominator((1/2^n)*sum(k=1, n, 2^k/k))) \\ Altug Alkan, Nov 20 2015

Crossrefs

See A046825, the main entry for this sequence. Cf. A046878.

Sequence in context: A352015 A225503 A302350 * A248267 A236415 A267831

Adjacent sequences: A046876 A046877 A046878 * A046880 A046881 A046882

Keyword

nonn,frac,easy,nice

Author

N. J. A. Sloane

Status

approved