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A203419 a(n) = A203418(n+1)/A203418(n).

%I A203419 #12 Feb 24 2024 11:03:45
%S A203419 2,8,15,48,1152,19200,62370,322560,17418240,567705600,2481078600,
%T A203419 16907304960,1504935936000,8799558768000,76435881984000,
%U A203419 819678899239200,10176845001523200,2169274855587840000,215013524533936128000
%N A203419 a(n) = A203418(n+1)/A203418(n).
%H A203419 G. C. Greubel, <a href="/A203419/b203419.txt">Table of n, a(n) for n = 1..350</a>
%t A203419 composite = Select[Range[100], CompositeQ]; (* A002808 *)
%t A203419 z = 20;
%t A203419 f[j_]:= composite[[j]];
%t A203419 v[n_]:= Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}];
%t A203419 d[n_]:= Product[(i-1)!, {i, 1, n}];
%t A203419 Table[v[n], {n,z}]           (* A203418 *)
%t A203419 Table[v[n+1]/v[n], {n,z}]    (* this sequence *)
%t A203419 Table[v[n]/d[n], {n,z}]      (* A203420 *)
%o A203419 (Magma)
%o A203419 A002808:=[n: n in [2..250] | not IsPrime(n)];
%o A203419 a:= func< n | (&*[A002808[n+1] - A002808[j+1]: j in [0..n-1]]) >;
%o A203419 [a(n): n in [1..40]]; // _G. C. Greubel_, Feb 24 2024
%o A203419 (SageMath)
%o A203419 A002808=[n for n in (2..250) if not is_prime(n)]
%o A203419 def a(n): return product(A002808[n] - A002808[j] for j in range(n))
%o A203419 [a(n) for n in range(1,41)] # _G. C. Greubel_, Feb 24 2024
%Y A203419 Cf. A000040, A002808, A003418, A203418, A203420.
%K A203419 nonn
%O A203419 1,1
%A A203419 _Clark Kimberling_, Jan 02 2012