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A203465 a(n) = A203305(n)/A000178(n) where A000178 are superfactorials.

%I A203465 #15 Sep 19 2023 03:41:07
%S A203465 1,2,24,5376,72253440,192663508746240,345230911480770991226880,
%T A203465 1436598918224589625071929521581588480,
%U A203465 48781096034575545526663437061892218092260229434572800
%N A203465 a(n) = A203305(n)/A000178(n) where A000178 are superfactorials.
%H A203465 G. C. Greubel, <a href="/A203465/b203465.txt">Table of n, a(n) for n = 1..22</a>
%H A203465 R. Chapman, <a href="https://www.jstor.org/stable/2690667">A polynomial taking integer values</a>, Mathematics Magazine, 29 (1996), 121.
%t A203465 f[j_]:= 2^j - 1; z = 10;
%t A203465 v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
%t A203465 d[n_]:= Product[(i-1)!, {i,n}]
%t A203465 Table[v[n], {n,z}]         (* A203305 *)
%t A203465 Table[v[n]/d[n], {n,z}]    (* A203465 *)
%o A203465 (Magma) F:= Factorial; [1] cat [(&*[(&*[2^(k+1) - 2^(j): j in [1..k]])/Factorial(k): k in [1..n-1]]): n in [2..20]]; // _G. C. Greubel_, Sep 19 2023
%o A203465 (SageMath) f=factorial; [product(product(2^(k+1) - 2^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 A203465 Cf. A203305.
%K A203465 nonn
%O A203465 1,2
%A A203465 _Clark Kimberling_, Jan 02 2012
%E A203465 Name edited by _Michel Marcus_, May 17 2019