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%I #19 Sep 08 2022 08:45:58
%S 1,1,4,36,144,3600,14400,705600,2822400,228614400,914457600,
%T 110649369600,442597478400,74798973849600,299195895398400,
%U 67319076464640000,269276305858560000,77820852393123840000,311283409572495360000,112373310855670824960000
%N a(n) = (n!/floor(n/2)!)^2.
%H Vincenzo Librandi, <a href="/A193282/b193282.txt">Table of n, a(n) for n = 0..400</a>
%F a(n) = A056040(n)*A000142(n).
%F a(n) = A081125(n)^2.
%F a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*A195009(n,k).
%F a(n) = n!^2*[x^n] (1+x)*BesselI(0,2*x). Here [x^n]f(x) denotes the coefficient of x^n in f(x).
%F Conjecture: a(n) + 8*a(n-1) - 4*(n-2)*(n+2)*a(n-2) + 16*(-2*n^2 + 6*n - 3)*a(n-3) - 64*(n-3)^2*a(n-4) = 0. - _R. J. Mathar_, Oct 03 2014
%p A193282 := n -> (n!/iquo(n,2)!)^2;
%t Table[(n!/(Floor[n/2]!))^2,{n,0,20}] (* _Harvey P. Dale_, Jul 30 2020 *)
%o (Magma) [(Factorial(n)/Factorial(Floor(n/2)))^2: n in [0..20]]; // _Vincenzo Librandi_, Sep 11 2011
%Y Cf. A000142, A056040, A195009.
%K nonn
%O 0,3
%A _Peter Luschny_, Sep 08 2011