%I #14 Jul 23 2017 13:14:20
%S 1,8,960,3870720,535088332800,4746447547269120000,
%T 2251903055463146166681600000,101133031075657891684280256430080000000,
%U 764075218501479062478490016486870993810227200000000,510692344365454233151092604262379676645631378616169267200000000000
%N a(n) = Product_{2 <= i < j <= n+1} (prime(i) + prime(j)).
%C 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 a:= n-> mul(mul(ithprime(i)+ithprime(j), i=2..j-1), j=3..n+1):
%p seq(a(n), n=1..10); # _Alois P. Heinz_, Jul 23 2017
%t f[j_] := Prime[j + 1]; z = 17;
%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}] (* A203524 *)
%t Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}] (* A203525 *)
%t Table[v[n]/d[n], {n, 1, 20}] (* A203526 *)
%Y Cf. A000040, A203315, A203525, A203526.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 03 2012
%E Name edited by _Alois P. Heinz_, Jul 23 2017
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