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A275329
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a(n) = (2+[n/2])*n!/((1+[n/2])*[n/2]!^2).
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1
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2, 2, 3, 9, 8, 40, 25, 175, 84, 756, 294, 3234, 1056, 13728, 3861, 57915, 14300, 243100, 53482, 1016158, 201552, 4232592, 764218, 17577014, 2912168, 72804200, 11143500, 300874500, 42791040, 1240940160, 164812365, 5109183315, 636438060, 21002455980, 2463251010
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internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = A056040(n)*(2+[n/2])/(1+[n/2]).
a(2*n+1) = (n+2)*binomial(2*n+1, n+1) = A189911(2*n+1).
a(2*n-3) = n*binomial(2*n-3, n-1) = A097070(n) for n>=2.
a(2*n+2) = (n+3)*binomial(2*n+2, n+1)/(n+2) = A038665(n).
Sum_{n>=0} 1/a(n) = 16/3 - 40*Pi/(9*sqrt(3)) + 4*Pi^2/9. - Amiram Eldar, Aug 20 2022
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MAPLE
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a := n -> (2+iquo(n, 2))*n!/((1+iquo(n, 2))*iquo(n, 2)!^2):
seq(a(n), n=0..34);
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PROG
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(Sage)
x, n, k = 1, 1, 2
while True:
yield x * k
if is_odd(n):
x *= n
else:
k += 1
x = (x<<2)//(n+2)
n += 1
a = A275329(); print([next(a) for _ in range(37)])
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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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