|
%I #12 Jan 08 2024 10:57:02
%S 1,1,1,0,-12,-54,-2628,-77616,-86688,-3837456,-6295968,-5189982336,
%T -773398378368,-60614059968,-710855139456,-274917009540096,
%U -70812306032928768,-20799092342375424,-53842565061863424,-48391925819124400128,-3845848802828440117248,-64663161151688486424576,-30966053952082739476783104
%N Numerator of Sum_{k=0..n} binomial(n,k)*(-1)^k/(k^2+1).
%H Philippe Flajolet and Robert Sedgewick, <a href="https://doi.org/10.1016/0304-3975(94)00281-M">Mellin transforms and asymptotics: Finite differences and Rice's integrals</a>, Theoretical Computer Science 144.1-2 (1995): 101-124.
%e 1, 1/2, 1/5, 0, -12/85, -54/221, -2628/8177, -77616/204425, -86688/204425, ...
%p T:=n->add(binomial(n,k)*(-1)^k/(k^2+1),k=0..n);
%t Table[Sum[(Binomial[n,k](-1)^k)/(k^2+1),{k,0,n}],{n,0,30}]//Numerator (* _Harvey P. Dale_, Jul 25 2020 *)
%o (PARI) a(n) = numerator(sum(k=0, n, binomial(n,k)*(-1)^k/(k^2+1))); \\ _Michel Marcus_, Jan 08 2024
%Y Cf. A190950.
%K sign,frac
%O 0,5
%A _N. J. A. Sloane_, May 24 2011
|
