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A004732
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Numerator of n!!/(n+3)!!.
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2
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1, 1, 2, 1, 8, 5, 16, 7, 128, 21, 256, 33, 1024, 429, 2048, 715, 32768, 2431, 65536, 4199, 262144, 29393, 524288, 52003, 4194304, 185725, 8388608, 334305, 33554432, 9694845, 67108864, 17678835, 2147483648
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OFFSET
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0,3
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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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MAPLE
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f:= proc(n) local m, r;
m:= floor(n/2);
if n::even then 2^(2*m - padic:-ordp(binomial(2*m+1, m), 2) - padic:-ordp(m+1, 2))
else
r:= binomial(2*m+2, m+1)/(m+2);
r/2^padic:-ordp(r, 2);
fi
end proc:
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MATHEMATICA
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Numerator[Table[n!!/(n+3)!!, {n, 0, 40}]] (* Harvey P. Dale, Nov 26 2015 *)
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PROG
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(PARI) a(n) = numerator(prod(i=0, floor((n-1)/2), n-2*i)/prod(i=0, floor((n+2)/2), n+3-2*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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