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

0,4

Comments

a(n) is also the numerator 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) = 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

Example

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

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 *)

Prog

(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

Crossrefs

See A046825, the main entry for this sequence. Cf. A046879.

Sequence in context: A187876 A179951 A198192 * A375600 A357114 A078335

Adjacent sequences: A046875 A046876 A046877 * A046879 A046880 A046881

Keyword

nonn,frac,easy,nice

Author

N. J. A. Sloane

Status

approved