This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180064 #13 Oct 19 2023 17:42:43
%S A180064 1,1,1,1,4,4,36,36,576,576,14400,14400,518400,518400,25401600,
%T A180064 25401600,1625702400,1625702400,131681894400,131681894400,
%U A180064 13168189440000,13168189440000,1593350922240000,1593350922240000,229442532802560000,229442532802560000
%N A180064 a(n) = n!/A056040(n).
%C A180064 From _Emeric Deutsch_, Dec 24 2008 [edited and moved here by _Andrey Zabolotskiy_, Oct 19 2023]: (Start)
%C A180064 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.
%C A180064 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.
%C A180064 a(n+1) = A134434(n,0). (End)
%F A180064 a(n) = A000142(n) / A056040(n).
%F A180064 a(n) = floor(n/2)!^2. - _Peter Luschny_, Aug 23 2010
%p A180064 A180064 := n -> iquo(n,2)!^2; # _Peter Luschny_, Aug 23 2010
%t A180064 f[n_] := 2^(n - Mod[n, 2])*Product[k^((-1)^(k+1)), {k,n}]; Array[ #!/f@# &, 25, 0]
%Y A180064 Cf. A000142, A056040, A134434.
%K A180064 easy,nonn
%O A180064 0,5
%A A180064 _Robert G. Wilson v_, Aug 08 2010