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v(n)/A000178(n); v=A203521 and A000178=(superfactorials).
3

%I #7 Jan 14 2013 08:43:50

%S 1,5,140,25200,55036800,951035904000,222618484408320000,

%T 440079343769868042240000,12254449406615745504215040000000,

%U 7909254579604123100510930935480320000000,48073937540175558516708030362614204937011200000000

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

%C It is conjectured that every term of A203523 is an integer.

%t f[j_] := Prime[j]; z = 15;

%t v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]

%t d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)

%t Table[v[n], {n, 1, z}] (* A203521 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203522 *)

%t Table[v[n]/d[n], {n, 1, 20}] (* A203523 *)

%Y Cf. A203522, A203523, A000040, A093883.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 03 2012