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

%I A046878 #36 Feb 16 2025 08:32:39
%S A046878 0,1,1,5,2,8,13,151,32,83,73,1433,647,15341,28211,10447,1216,19345,
%T A046878 18181,651745,1542158,1463914,2786599,122289917,29229544,140001721,
%U A046878 134354573,774885169,745984697,41711914513,80530073893,4825521853483
%N A046878 Numerator of (1/n)*Sum_{k=0..n-1} 1/binomial(n-1,k) for n>0 else 0.
%C A046878 a(n) is also the numerator of (1/2^n)*Sum_{k=1..n} 2^k/k. - _Groux Roland_, Jan 13 2009
%H A046878 Seiichi Manyama, <a href="/A046878/b046878.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from T. D. Noe)
%H A046878 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeibnizHarmonicTriangle.html">Leibniz Harmonic Triangle</a>
%F A046878 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
%F A046878 a(n) = numerator(-2*LerchPhi(2,1,n+1)-i*Pi/2^n). - _Peter Luschny_, Nov 20 2015
%e A046878 Rational sequence starts: 0, 1, 1, 5/6, 2/3, 8/15, 13/30, 151/420, 32/105,...
%p A046878 a := n -> -2*LerchPhi(2,1,n+1)-I*Pi/2^n:
%p A046878 seq(numer(simplify(a(n))),n=0..31); # _Peter Luschny_, Nov 20 2015
%t A046878 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 *)
%o A046878 (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 */
%o A046878 (PARI) vector(40, n, n--; numerator((1/2^n)*sum(k=1, n, 2^k/k))) \\ _Altug Alkan_, Nov 20 2015
%Y A046878 See A046825, the main entry for this sequence. Cf. A046879.
%K A046878 nonn,frac,easy,nice
%O A046878 0,4
%A A046878 _N. J. A. Sloane_