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A190906 a(n) = gcd(n! / floor(n/2)!^2, 3^n).

%I A190906 #19 Aug 02 2019 21:18:25
%S A190906 1,1,1,3,3,3,1,1,1,9,9,9,3,3,3,9,9,9,1,1,1,3,3,3,1,1,1,27,27,27,9,9,9,
%T A190906 27,27,27,3,3,3,9,9,9,3,3,3,27,27,27,9,9,9,27,27,27,1,1,1,3,3,3,1,1,1,
%U A190906 9,9,9,3,3,3,9,9,9,1,1,1,3,3,3,1,1,1
%N A190906 a(n) = gcd(n! / floor(n/2)!^2, 3^n).
%H A190906 Charles R Greathouse IV, <a href="/A190906/b190906.txt">Table of n, a(n) for n = 0..10000</a>
%F A190906 a(n) = gcd(A056040(n), 3^n).
%F A190906 a(n) <= n. - _Charles R Greathouse IV_, Jun 30 2011
%F A190906 From _Johannes W. Meijer_, Jun 30 2011: (Start)
%F A190906 a(3*n) = a(3*n+1) = a(3*n+2) = A010684(n)*a(n) for n > 1 with a(0) = a(1) = a(2) = 1.
%F A190906 a(9*n+3) = a(9*n+4) = a(9*n+5) = 3*a(n).
%F A190906 a(9*n) = a(9*n+1) = a(9*n+2) = a(9*n+6) = a(9*n+7) = a(9*n+8) = A010690(n)*a(n). (End)
%p A190906 A190906 := n -> igcd(n!/iquo(n,2)!^2,3^n): seq(A190906(n),n=0..80);
%t A190906 sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; a[n_] := GCD[sf[n], 3^n]; Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Jul 29 2013 *)
%o A190906 (PARI) a(n)=gcd(n!/(n\2)!^2, 3^n) \\ _Charles R Greathouse IV_, Jun 30 2011
%o A190906 (PARI) a(n)=my(s);while(n\=3,s+=n%2);3^s \\ _Charles R Greathouse IV_, Jun 30 2011
%Y A190906 Cf. A060632.
%K A190906 nonn,easy,look,hear
%O A190906 0,4
%A A190906 _Peter Luschny_, Jun 30 2011