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A329965
a(n) = ((1+n)*floor(1+n/2))*(n!/floor(1+n/2)!)^2.
1
1, 2, 6, 72, 240, 7200, 25200, 1411200, 5080320, 457228800, 1676505600, 221298739200, 821966745600, 149597947699200, 560992303872000, 134638152929280000, 508633022177280000, 155641704786247680000, 591438478187741184000, 224746621711341649920000
OFFSET
0,2
FORMULA
a(n) = n!*A212303(n+1).
a(n) = (n+1)!*A057977(n).
a(n) = A093005(n+1)*A262033(n)^2.
a(n) = A093005(n+1)*A329964(n).
a(2*n) = A052510(n) (n >= 0).
a(2*n+1) = A123072(n+1) (n >= 0).
a(n) = n! [x^n] (1 - sqrt(1 - 4*x^2) - 4*x^2*(1 - x - sqrt(1 - 4*x^2)))/(2*x^2*(1 - 4*x^2)^(3/2)).
MAPLE
A329965 := n -> ((1+n)*floor(1+n/2))*(n!/floor(1+n/2)!)^2:
seq(A329965(n), n=0..19);
MATHEMATICA
ser := Series[(1 - Sqrt[1 - 4 x^2] - 4 x^2 (1 - x - Sqrt[1 - 4 x^2]))/(2 x^2 (1 - 4 x^2)^(3/2)), {x, 0, 22}]; Table[n! Coefficient[ser, x, n], {n, 0, 20}]
Table[(1+n)Floor[1+n/2](n!/Floor[1+n/2]!)^2, {n, 0, 30}] (* Harvey P. Dale, Oct 01 2023 *)
PROG
(Python)
def A329965():
x, n = 1, 1
while true:
yield x
m = n if n % 2 else 4/(n+2)
n += 1
x *= m * n
a = A329965(); [next(a) for i in range(36)]
KEYWORD
nonn
AUTHOR
Peter Luschny, Dec 04 2019
STATUS
approved