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A203431 a(n) = v(n+1)/v(n), where v=A203430.

%I A203431 #16 Jun 09 2025 09:04:11
%S A203431 2,3,30,72,1440,4536,142560,544320,23950080,106142400,6107270400,
%T A203431 30569011200,2198617344000,12197035468800,1061932177152000,
%U A203431 6440034727526400,662645678542848000,4347023441080320000
%N A203431 a(n) = v(n+1)/v(n), where v=A203430.
%H A203431 G. C. Greubel, <a href="/A203431/b203431.txt">Table of n, a(n) for n = 1..300</a>
%t A203431 f[j_]:= j + Floor[j/2]; z = 20;
%t A203431 v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
%t A203431 d[n_]:= Product[(i-1)!, {i,n}]
%t A203431 Table[v[n], {n,z}]            (* A203430 *)
%t A203431 Table[v[n+1]/v[n], {n,z}]     (* this sequence *)
%t A203431 Table[v[n]/d[n], {n,z}]       (* A203432 *)
%o A203431 (Magma)
%o A203431 A203431:= func< n | n eq 1 select 2 else (&*[n-j+Floor((n+1)/2)-Floor((j+1)/2): j in [0..n-1]]) >;
%o A203431 [A203431(n): n in [1..25]]; // _G. C. Greubel_, Sep 27 2023
%o A203431 (SageMath)
%o A203431 def A203431(n): return product(n-j+((n+1)//2)-((j+1)//2) for j in range(n))
%o A203431 [A203431(n) for n in range(1, 31)] # _G. C. Greubel_, Sep 27 2023
%Y A203431 Cf. A032766, A203430, A203432.
%K A203431 nonn
%O A203431 1,1
%A A203431 _Clark Kimberling_, Jan 02 2012
%E A203431 Typo in the definition corrected by _Vaclav Kotesovec_, Jun 09 2025