A355989 a(n) = n! / (2 * floor(n/2)!).
1, 3, 6, 30, 60, 420, 840, 7560, 15120, 166320, 332640, 4324320, 8648640, 129729600, 259459200, 4410806400, 8821612800, 167610643200, 335221286400, 7039647014400, 14079294028800, 323823762662400, 647647525324800, 16191188133120000, 32382376266240000
Offset: 2
Programs
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Mathematica
a[n_] := n!/(2 * Floor[n/2]!); Array[a, 25, 2] (* Amiram Eldar, Jul 22 2022 *)
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PARI
a(n) = n!/(2*(n\2)!);
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^2)*(exp(x^2)-1)/(2*(1-x)))) -
Python
from math import factorial, floor def a(n): return int(factorial(n)/(2*factorial(floor(n/2)))) print([a(n) for n in range(2, 30)]) # Javier Rivera Romeu, Jul 22 2022
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Python
from sympy import rf def A355989(n): return rf((m:=n+1>>1)+(n+1&1),m)>>1 # Chai Wah Wu, Jul 22 2022
Formula
E.g.f.: (1 - x^2) * (exp(x^2) - 1)/(2 * (1 - x)).
a(n) = A081125(n)/2.
From Amiram Eldar, Jul 26 2022: (Start)
Sum_{n>=2} 1/a(n) = 3*exp(1/4)*sqrt(Pi)*erf(1/2) - 2, where erf is the error function.
Sum_{n>=2} (-1)^n/a(n) = 2 - exp(1/4)*sqrt(Pi)*erf(1/2). (End)