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A329965
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a(n) = ((1+n)*floor(1+n/2))*(n!/floor(1+n/2)!)^2.
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1
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1, 2, 6, 72, 240, 7200, 25200, 1411200, 5080320, 457228800, 1676505600, 221298739200, 821966745600, 149597947699200, 560992303872000, 134638152929280000, 508633022177280000, 155641704786247680000, 591438478187741184000, 224746621711341649920000
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OFFSET
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0,2
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LINKS
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FORMULA
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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)).
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MAPLE
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A329965 := n -> ((1+n)*floor(1+n/2))*(n!/floor(1+n/2)!)^2:
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MATHEMATICA
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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 *)
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PROG
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(Python)
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)]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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