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A240988
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Denominators of the (reduced) rationals (((n-1)!!)/(n!! * 2^((1 + (-1)^n)/2)))^((-1)^n), where n is a positive integer.
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1
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1, 4, 2, 16, 8, 32, 16, 256, 128, 512, 256, 2048, 1024, 4096, 2048, 65536, 32768, 131072, 65536, 524288, 262144, 1048576, 524288, 8388608, 4194304, 16777216, 8388608, 67108864, 33554432, 134217728, 67108864, 4294967296, 2147483648, 8589934592, 4294967296
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OFFSET
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1,2
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COMMENTS
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Numerators for this sequence are the swinging factorial A163590, starting from n = 1.
The terms are all powers of 2 (A000079).
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LINKS
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FORMULA
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a(n) = denominator((((n-1)!!)/(n!! * 2^((1 + (-1)^n)/2)))^((-1)^n)).
a(n) = denominator(g(1, n)) where g(m, n) = m if m = n; m/(2 * g(m + 1, n) otherwise.
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EXAMPLE
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For n = 1, a(1) = 1.
For n = 2, a(2) = 2 * 2 = 4.
For n = 6, a(6) = 2 * 2 * 4 * 2 = 32.
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MAPLE
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f:= n -> denom(((doublefactorial(n-1)) / (doublefactorial(n)*2^((1+(-1)^n)/2)))^((-1)^n)):
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PROG
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(PARI)
df(n) = prod(i=0, floor((n-1)/2), n-2*i) \\ Double factorial (n!!)
a(n) = denominator(((df(n-1)) / (df(n)*2^((1+(-1)^n)/2)))^((-1)^n))
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CROSSREFS
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KEYWORD
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frac,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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