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A067667
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a(n) = (2^n)!/2^(2^n-1).
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7
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OFFSET
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0,3
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COMMENTS
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a(n) is also the number of knockout tournament seedings with 2^n teams. - Alexander Karpov, Aug 09 2015
a(n) is also the number of heap-ordered binomial trees of order n (i.e., binomial heaps with 2^n nodes), see the Mark R. Brown reference.
a(n) is also the largest odd divisor of (2^n)!. (End)
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LINKS
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FORMULA
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a(n) = (2^n)!/2^(2^n-1).
a(n) = (2^n-1)!!*a(n-1).
a(n) = binomial(2^n-1, 2^(n-1)-1)*(a(n-1))^2 = A069954(n-1) * (a(n-1))^2.
(End)
a(n) = Product_{odd k < 2^n} k^(n - floor(log_2(k))). - Harry Richman, May 18 2023
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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