A046878 Numerator of (1/n)*Sum_{k=0..n-1} 1/binomial(n-1,k) for n>0 else 0.

0, 1, 1, 5, 2, 8, 13, 151, 32, 83, 73, 1433, 647, 15341, 28211, 10447, 1216, 19345, 18181, 651745, 1542158, 1463914, 2786599, 122289917, 29229544, 140001721, 134354573, 774885169, 745984697, 41711914513, 80530073893, 4825521853483

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy
• nice

Comments

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

Examples

			Rational sequence starts: 0, 1, 1, 5/6, 2/3, 8/15, 13/30, 151/420, 32/105,...
		

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. A046879.

Programs

Maple

a := n -> -2*LerchPhi(2,1,n+1)-I*Pi/2^n:
seq(numer(simplify(a(n))),n=0..31); # Peter Luschny, Nov 20 2015

Mathematica

a[0] = 0; a[n_] := (1/n) Sum[1/Binomial[n-1, k], {k, 0, n-1}] // Numerator; Table[a[n], {n, 0, 31}] (* Jean-François Alcover, Sep 28 2016 *)

Maxima

a(n):=if n=0 then 0 else num((-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(40, n, n--; numerator((1/2^n)*sum(k=1, n, 2^k/k))) \\ Altug Alkan, Nov 20 2015

Formula

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

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