A180064 a(n) = n!/A056040(n).

1, 1, 1, 1, 4, 4, 36, 36, 576, 576, 14400, 14400, 518400, 518400, 25401600, 25401600, 1625702400, 1625702400, 131681894400, 131681894400, 13168189440000, 13168189440000, 1593350922240000, 1593350922240000, 229442532802560000, 229442532802560000

Offset: 0

Author

Robert G. Wilson v, Aug 08 2010

Keywords

• easy
• nonn

Comments

From Emeric Deutsch, Dec 24 2008 [edited and moved here by Andrey Zabolotskiy, Oct 19 2023]: (Start)

a(n+1) is the number of permutations of {1,2,...,n} with no even entry followed by a smaller entry. Example: a(5)=4 because we have 1234, 1324, 3124 and 2314.

a(n+1) is the number of permutations p of {1,2,...,n} such that p(j) is odd whenever j is even. Example: a(5)=4 because we have 4123, 2143, 2341 and 4321.

a(n+1) = A134434(n,0). (End)

Crossrefs

Cf. A000142, A056040, A134434.

Programs

Maple

A180064 := n -> iquo(n,2)!^2; # Peter Luschny, Aug 23 2010

Mathematica

f[n_] := 2^(n - Mod[n, 2])*Product[k^((-1)^(k+1)), {k,n}]; Array[ #!/f@# &, 25, 0]

Formula

a(n) = A000142(n) / A056040(n).

a(n) = floor(n/2)!^2. - Peter Luschny, Aug 23 2010