login
Bisection of A000255.
0

%I #13 Jul 27 2022 08:49:33

%S 1,3,53,2119,148329,16019531,2467007773,513137616783,138547156531409,

%T 47106033220679059,19690321886243846661,9923922230666898717143,

%U 5934505493938805432851513,4154153845757163802996059099

%N Bisection of A000255.

%F a(n) = (2*n + 1)!*hypergeom([-2*n], [-2*n - 1], -1). - _Peter Luschny_, Nov 02 2018

%F D-finite with recurrence a(n) +(-4*n^2-2*n+1)*a(n-1) +2*n*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Jul 27 2022

%p a := n -> (2*n+1)!*hypergeom([-2*n],[-2*n-1],-1):

%p seq(simplify(a(n)), n=0..13); # _Peter Luschny_, Nov 02 2018

%t a[n_] := (2n)! SeriesCoefficient[E^-x / (1-x)^2, {x, 0, 2n}];

%t Table[a[n], {n, 0, 13}] (* _Jean-François Alcover_, Jun 11 2019 *)

%Y Cf. A000255.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 21 2004

%E More terms from _Hugo Pfoertner_, Nov 26 2004