|
%I #34 Dec 02 2018 09:23:32
%S 1,1,1,6,3,15,30,420,105,315,315,6930,3465,90090,180180,72072,9009,
%T 153153,153153,5819814,14549535,14549535,29099070,1338557220,
%U 334639305,1673196525,1673196525,10039179150,10039179150,582272390700,1164544781400
%N Denominator of (1/n)*Sum_{k=0..n-1} 1/binomial(n-1,k) for n>0 else 1.
%C For n>=1 a(n) is the denominator of (1/2^n)*Sum_{k=1..n} 2^k/k. - _Groux Roland_, Jan 13 2009
%H Seiichi Manyama, <a href="/A046879/b046879.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from T. D. Noe)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeibnizHarmonicTriangle.html">Leibniz Harmonic Triangle</a>
%F 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
%F a(n) = denominator(-2*LerchPhi(2,1,n+1)-i*Pi/2^n). - _Peter Luschny_, Nov 20 2015
%p a := n -> -2*LerchPhi(2,1,n+1)-I*Pi/2^n:
%p seq(denom(simplify(a(n))),n=0..30); # _Peter Luschny_, Nov 20 2015
%t Denominator[Simplify[-2*LerchPhi[2, 1, # + 1] - I*Pi/2^#]] & /@
%t Range[0, 100] (* _Julien Kluge_, Jul 21 2016 *)
%o (Maxima)
%o 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 */
%o (PARI) vector(30, n, n--; denominator((1/2^n)*sum(k=1, n, 2^k/k))) \\ _Altug Alkan_, Nov 20 2015
%Y See A046825, the main entry for this sequence. Cf. A046878.
%K nonn,frac,easy,nice
%O 0,4
%A _N. J. A. Sloane_
|
