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A355989 a(n) = n! / (2 * floor(n/2)!).

%I A355989 #31 Jul 26 2022 12:46:53
%S A355989 1,3,6,30,60,420,840,7560,15120,166320,332640,4324320,8648640,
%T A355989 129729600,259459200,4410806400,8821612800,167610643200,335221286400,
%U A355989 7039647014400,14079294028800,323823762662400,647647525324800,16191188133120000,32382376266240000
%N A355989 a(n) = n! / (2 * floor(n/2)!).
%F A355989 E.g.f.: (1 - x^2) * (exp(x^2) - 1)/(2 * (1 - x)).
%F A355989 a(n) = A081125(n)/2.
%F A355989 From _Amiram Eldar_, Jul 26 2022: (Start)
%F A355989 Sum_{n>=2} 1/a(n) = 3*exp(1/4)*sqrt(Pi)*erf(1/2) - 2, where erf is the error function.
%F A355989 Sum_{n>=2} (-1)^n/a(n) = 2 - exp(1/4)*sqrt(Pi)*erf(1/2). (End)
%t A355989 a[n_] := n!/(2 * Floor[n/2]!); Array[a, 25, 2] (* _Amiram Eldar_, Jul 22 2022 *)
%o A355989 (PARI) a(n) = n!/(2*(n\2)!);
%o A355989 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2)*(exp(x^2)-1)/(2*(1-x))))
%o A355989 (Python)
%o A355989 from math import factorial, floor
%o A355989 def a(n): return int(factorial(n)/(2*factorial(floor(n/2))))
%o A355989 print([a(n) for n in range(2, 30)]) # _Javier Rivera Romeu_, Jul 22 2022
%o A355989 (Python)
%o A355989 from sympy import rf
%o A355989 def A355989(n): return rf((m:=n+1>>1)+(n+1&1),m)>>1 # _Chai Wah Wu_, Jul 22 2022
%Y A355989 Column 2 of A355996.
%Y A355989 Cf. A355990, A355991,
%K A355989 nonn,easy
%O A355989 2,2
%A A355989 _Seiichi Manyama_, Jul 22 2022