OFFSET
2,2
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)
MATHEMATICA
a[n_] := n!/(2 * Floor[n/2]!); Array[a, 25, 2] (* Amiram Eldar, Jul 22 2022 *)
PROG
(PARI) a(n) = n!/(2*(n\2)!);
(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
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 22 2022
STATUS
approved