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A318910
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a(n) is the nearest integer to binomial(n,n/2) = n!/((n/2)!)^2.
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0
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1, 1, 2, 3, 6, 11, 20, 37, 70, 132, 252, 482, 924, 1778, 3432, 6639, 12870, 24994, 48620, 94716, 184756, 360821, 705432, 1380533, 2704156, 5301248, 10400600, 20419624, 40116600, 78861995, 155117520, 305272239, 601080390, 1184086260, 2333606220, 4601020897, 9075135300
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OFFSET
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0,3
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COMMENTS
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If we consider binomial(n,x) as a real-valued function of x, then a(n) is the maximum value of binomial(n,x) (always obtained by x = n/2), rounded. Here binomial(n,x) must be understood as Gamma(n+1)/(Gamma(x+1)*Gamma(n-x+1)).
A093581 actually has already mentioned a geometric interpretation of this sequence.
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LINKS
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FORMULA
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a(n) ~ 2^n/sqrt(n*Pi/2).
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EXAMPLE
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a(1) = round(1!/(0.5!)^2) = round(4/Pi) = round(1.2732395...) = 1.
a(3) = round(3!/(1.5!)^2) = round(32/(3*Pi)) = round(3.3953054...) = 3.
a(5) = round(5!/(2.5!)^2) = round(512/(15*Pi)) = round(10.8649774...) = 11.
a(7) = round(7!/(3.5!)^2) = round(4096/(35*Pi)) = round(37.2513512...) = 37.
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PROG
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(PARI) a(n) = round(gamma(n+1)/gamma(n/2+1)^2)
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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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