A004732 Numerator of n!!/(n+3)!!.

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

Offset

0,3

References

S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996.

Links

Robert Israel, Table of n, a(n) for n = 0..3327

S. Janson, On the traveling fly problem

Formula

From Robert Israel, Jan 07 2019: (Start)

a(2*m) = 2^(2*m+1 - A048881(m) - A007814(m+1)).

a(2*m+1) = A000265(A000108(m+1)). (End)

Maple

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:
map(f, [$0..50]); # Robert Israel, Jan 07 2019

Mathematica

Numerator[Table[n!!/(n+3)!!, {n, 0, 40}]] (* Harvey P. Dale, Nov 26 2015 *)

Prog

(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

Crossrefs

Cf. A000108, A000265, A004733, A007814, A048881.

Sequence in context: A344163 A199468 A337684 * A297809 A160641 A011244

Adjacent sequences: A004729 A004730 A004731 * A004733 A004734 A004735

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved