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A203524 a(n) = Product_{2 <= i < j <= n+1} (prime(i) + prime(j)).

%I A203524 #14 Jul 23 2017 13:14:20
%S A203524 1,8,960,3870720,535088332800,4746447547269120000,
%T A203524 2251903055463146166681600000,101133031075657891684280256430080000000,
%U A203524 764075218501479062478490016486870993810227200000000,510692344365454233151092604262379676645631378616169267200000000000
%N A203524 a(n) = Product_{2 <= i < j <= n+1} (prime(i) + prime(j)).
%C A203524 Each term divides its successor, as in A203525. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n); as in A203526. See A093883 for a guide to related sequences.
%p A203524 a:= n-> mul(mul(ithprime(i)+ithprime(j), i=2..j-1), j=3..n+1):
%p A203524 seq(a(n), n=1..10);  # _Alois P. Heinz_, Jul 23 2017
%t A203524 f[j_] := Prime[j + 1]; z = 17;
%t A203524 v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203524 d[n_] := Product[(i - 1)!, {i, 1, n}]    (* A000178 *)
%t A203524 Table[v[n], {n, 1, z}]                   (* A203524 *)
%t A203524 Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}]  (* A203525 *)
%t A203524 Table[v[n]/d[n], {n, 1, 20}]             (* A203526 *)
%Y A203524 Cf. A000040, A203315, A203525, A203526.
%K A203524 nonn
%O A203524 1,2
%A A203524 _Clark Kimberling_, Jan 03 2012
%E A203524 Name edited by _Alois P. Heinz_, Jul 23 2017