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A203314 a(n) = A080358(n)/A000178(n) where A000178 are superfactorials.

%I A203314 #10 May 17 2019 05:23:54
%S A203314 1,1,3,20,1440,126720,106444800,92649553920,800492145868800,
%T A203314 169546981039511961600,22908645527719529813114880,
%U A203314 98973345879641681792154678067200,1436275858228814897897209896513621196800
%N A203314 a(n) = A080358(n)/A000178(n) where A000178 are superfactorials.
%H A203314 R. Chapman, <a href="https://www.jstor.org/stable/2690667">A polynomial taking integer values</a>, Mathematics Magazine, 29 (1996), 121.
%t A203314 f[j_] := Prime[j]; z = 15;
%t A203314 v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203314 d[n_] := Product[(i - 1)!, {i, 1, n}]
%t A203314 Table[v[n], {n, 1, z}]              (* A080358 *)
%t A203314 Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A086803 *)
%t A203314 Table[v[n]/d[n], {n, 1, 20}]        (* A203314 *)
%Y A203314 Cf. A080358, A000178, A000040.
%K A203314 nonn
%O A203314 1,3
%A A203314 _Clark Kimberling_, Jan 01 2012
%E A203314 Name edited by _Michel Marcus_, May 17 2019