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A203523 v(n)/A000178(n); v=A203521 and A000178=(superfactorials).

%I A203523 #7 Jan 14 2013 08:43:50
%S A203523 1,5,140,25200,55036800,951035904000,222618484408320000,
%T A203523 440079343769868042240000,12254449406615745504215040000000,
%U A203523 7909254579604123100510930935480320000000,48073937540175558516708030362614204937011200000000
%N A203523 v(n)/A000178(n); v=A203521 and A000178=(superfactorials).
%C A203523 It is conjectured that every term of A203523 is an integer.
%t A203523 f[j_] := Prime[j]; z = 15;
%t A203523 v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203523 d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)
%t A203523 Table[v[n], {n, 1, z}]                (* A203521 *)
%t A203523 Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)
%t A203523 Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)
%Y A203523 Cf. A203522, A203523, A000040, A093883.
%K A203523 nonn
%O A203523 1,2
%A A203523 _Clark Kimberling_, Jan 03 2012