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%I #25 Jun 18 2019 03:15:40
%S 1,1,1,1,1,4,4,36,18,64,576,14400,43200,518400,518400,5080320,
%T 12700800,1625702400,1625702400,131681894400,131681894400,
%U 627056640000,13168189440000,1593350922240000
%N a(n) = lcm(n^2, n!) / lcm(n^2, swinging_factorial(n)).
%C A divisibility sequence, i.e., if m|n then a(m)|a(n). Except for n = 9 the prime factors of A181858(n) are the primes <= floor((n-1)/2). Using this fact the divisibility property can be proved. - _Peter Luschny_, Jan 10 2011
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(n) = A181857(n) / A181860(n).
%p A181858 := n -> `if`(n=0, 1, ilcm(n^2,n!)/ilcm(n^2,n!/iquo(n,2)!^2));
%t a[n_] := If[n == 0, 1, LCM[n^2, n!]/LCM[n^2, n!/Quotient[n, 2]!^2]];
%t Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Jun 18 2019 *)
%o (PARI) a(n)=lcm(n^2,n!)/lcm(n!/(n\2)!^2,n^2) \\ _Charles R Greathouse IV_, Feb 01 2013
%Y Cf. A000290, A056040, A170826, A181857, A181860.
%K nonn
%O 0,6
%A _Peter Luschny_, Nov 21 2010
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