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A256881 a(n) = n!/ceiling(n/2).

%I A256881 #32 Feb 02 2023 02:24:06
%S A256881 1,2,3,12,40,240,1260,10080,72576,725760,6652800,79833600,889574400,
%T A256881 12454041600,163459296000,2615348736000,39520825344000,
%U A256881 711374856192000,12164510040883200,243290200817664000,4644631106519040000,102181884343418880000,2154334728240414720000
%N A256881 a(n) = n!/ceiling(n/2).
%C A256881 Original name was: n!/round(n/2). - _Robert Israel_, Sep 03 2018
%H A256881 Robert Israel, <a href="/A256881/b256881.txt">Table of n, a(n) for n = 1..450</a>
%H A256881 Pierre-Alain Sallard, <a href="/A256881/a256881_1.pdf">Sum of repeated integrals of sinh</a>.
%F A256881 a(2n) = 2*A009445(n) = A052612(2n-1) = A052616(2n-1) = A052849(2n-1) = A098558(2n-1) = A081457(3n-1) = A208529(2n+1) = A256031(2n-1).
%F A256881 a(2n+1) = A110468(n) = A107991(2n+2) = A229244(2n+1), n>=0.
%F A256881 From _Robert Israel_, Sep 03 2018: (Start)
%F A256881 E.g.f.: -(1+1/x)*log(1-x^2).
%F A256881 n*(n+1)*(n+2)*a(n)+(n+2)*a(n+1)-(n+3)*a(n+2)=0. (End)
%F A256881 a(n) = 2/([x^n](sinh(x) + x*exp(x))). - _Pierre-Alain Sallard_, Dec 15 2018
%F A256881 Sum_{n>=1} 1/a(n) = (3*e-1/e)/4 = (e + sinh(1))/2. - _Amiram Eldar_, Feb 02 2023
%p A256881 A256881 := n!/round(n/2);
%t A256881 Function[x, 1/x] /@
%t A256881 CoefficientList[Series[(Sinh[x] + x*Exp[x])/2, {x, 0, 20}], x] (* _Pierre-Alain Sallard_, Dec 15 2018 *)
%o A256881 (PARI) A256881(n)=n!/round(n/2)
%o A256881 (Magma) [Factorial(n)/Round(n/2): n in [1..30]]; // _Vincenzo Librandi_, Apr 23 2015
%Y A256881 Cf. A009445, A052612, A052616, A052849, A081457, A208529, A098558, A107991, A110468, A229244, A256031.
%K A256881 nonn
%O A256881 1,2
%A A256881 _M. F. Hasler_, Apr 22 2015
%E A256881 Definition clarified by _Robert Israel_, Sep 03 2018