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A004735
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Denominator of average distance traveled by n-dimensional fly.
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2
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1, 3, 4, 15, 8, 35, 64, 315, 128, 693, 512, 3003, 1024, 6435, 16384, 109395, 32768, 230945, 131072, 969969, 262144, 2028117, 2097152, 16900975, 4194304, 35102025, 16777216, 145422675, 33554432
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OFFSET
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1,2
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COMMENTS
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The average distance is actually d(n) = 2*n!!/(n+1)!! if n is odd, and d(n) = (1*Pi)*4*n!!/(n+1)!! if n is even. So a(n) = denominator(d(n)) if n is odd and a(n) = denominator(Pi*d(n)) if n is even. - Michel Marcus, May 24 2013
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REFERENCES
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S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996.
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LINKS
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FORMULA
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PROG
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(PARI) a(n) = {if (n % 2, eo = 2, eo = 4); denominator(eo*prod(i=0, floor((n-1)/2), n-2*i)/prod(i=0, floor(n/2), n+1-2*i)); } \\ Michel Marcus, May 24 2013
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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