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A203466 a(n) = A203306(n)/A000178(n) where A000178 are superfactorials.

%I A203466 #14 Sep 19 2023 03:41:18
%S A203466 1,1,10,15180,97199847360,124679879327832253286400,
%T A203466 2359315315713931476611812172370616909824000,
%U A203466 69427548091550819116702789435220590352184299509517898727953530880000000
%N A203466 a(n) = A203306(n)/A000178(n) where A000178 are superfactorials.
%H A203466 G. C. Greubel, <a href="/A203466/b203466.txt">Table of n, a(n) for n = 1..16</a>
%H A203466 R. Chapman, <a href="https://www.jstor.org/stable/2690667">A polynomial taking integer values</a>, Mathematics Magazine, 29 (1996), 121.
%t A203466 f[j_]:= j!; z = 10;
%t A203466 v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
%t A203466 d[n_]:= Product[(i-1)!, {i,n}]
%t A203466 Table[v[n], {n,z}]       (* A203306 *)
%t A203466 Table[v[n]/d[n], {n,z}]  (* A203466 *)
%o A203466 (Magma) F:= Factorial; [1] cat [(&*[(&*[F(k+1) - F(j): j in [1..k]])/Factorial(k): k in [1..n-1]]): n in [2..20]]; // _G. C. Greubel_, Sep 19 2023
%o A203466 (SageMath) f=factorial; [product(product(f(k+1) - f(j) for j in range(1, k+1))//factorial(k) for k in range(1, n)) for n in range(1,21)] # _G. C. Greubel_, Sep 19 2023
%Y A203466 Cf. A203306.
%K A203466 nonn
%O A203466 1,3
%A A203466 _Clark Kimberling_, Jan 02 2012
%E A203466 Name edited by _Michel Marcus_, May 17 2019