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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy
• nice

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

Crossrefs

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

Programs

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 *)

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

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