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A046879 Denominator of (1/n)*Sum_{k=0..n-1} 1/binomial(n-1,k) for n>0 else 1. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A335567 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

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)