A100444 Bisection of A000255.

1, 3, 53, 2119, 148329, 16019531, 2467007773, 513137616783, 138547156531409, 47106033220679059, 19690321886243846661, 9923922230666898717143, 5934505493938805432851513, 4154153845757163802996059099

Offset: 0

Author

N. J. A. Sloane, Nov 21 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A000255.

Programs

Maple

a := n -> (2*n+1)!*hypergeom([-2*n],[-2*n-1],-1):
seq(simplify(a(n)), n=0..13); # Peter Luschny, Nov 02 2018

Mathematica

a[n_] := (2n)! SeriesCoefficient[E^-x / (1-x)^2, {x, 0, 2n}];
Table[a[n], {n, 0, 13}] (* Jean-François Alcover, Jun 11 2019 *)

Formula

a(n) = (2*n + 1)!*hypergeom([-2*n], [-2*n - 1], -1). - Peter Luschny, Nov 02 2018

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

Extensions

More terms from Hugo Pfoertner, Nov 26 2004