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A046878 Numerator of (1/n)*Sum_{k=0..n-1} 1/binomial(n-1,k) for n>0 else 0. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 * A078335 A021658 A270859

Adjacent sequences:  A046875 A046876 A046877 * A046879 A046880 A046881

KEYWORD

nonn,frac,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 22:22 EDT 2021. Contains 348119 sequences. (Running on oeis4.)