This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A205825 #19 Feb 13 2023 02:56:43
%S A205825 1,1,2,3,12,20,120,210,1680,3024,30240,55440,665280,1235520,17297280,
%T A205825 32432400,518918400,980179200,17643225600,33522128640,670442572800,
%U A205825 1279935820800,28158588057600,53970627110400,1295295050649600,2490952020480000,64764752532480000
%N A205825 a(n) = n!/ceiling(n/2)!.
%F A205825 E.g.f.: (exp(x^2)*(x+1) -1)/x. - _Sergei N. Gladkovskii_, Oct 10 2012
%F A205825 Sum_{n>=0} 1/a(n) = 3/2 + 5*exp(1/4)*sqrt(Pi)*erf(1/2)/4, where erf is the error function. - _Amiram Eldar_, Feb 13 2023
%t A205825 Table[n!/Ceiling[n/2]!,{n,0,24}]
%Y A205825 Cf. A205785, A205786.
%K A205825 nonn
%O A205825 0,3
%A A205825 _Clark Kimberling_, Feb 01 2012
%E A205825 a(0)=1 prepended and e.g.f. edited by _Alois P. Heinz_, Sep 08 2015