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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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

Crossrefs

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

Programs

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 *)

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

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)