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A203687 Vandermonde sequence using x^2 - x*y + y^2 applied to (1,2,6,...,n!).

%I A203687 #15 Nov 25 2021 17:32:27
%S A203687 1,3,2604,358528427712,12031987952968690199349362688,
%T A203687 370754012130869137189065686833099372581714820267297996800,
%U A203687 84815080863788633556908198622861272366206888854108620395778065239463085651541566677024367443968000000
%N A203687 Vandermonde sequence using x^2 - x*y + y^2 applied to (1,2,6,...,n!).
%C A203687 See A093883 for a discussion and guide to related sequences.
%t A203687 f[j_] := j!; z = 8;
%t A203687 u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2,
%t A203687   {j, 1, k - 1}]
%t A203687 v[n_] := Product[u[n], {k, 2, n}]
%t A203687 Table[v[n], {n, 1, z}]          (* A203687 *)
%t A203687 Table[v[n + 1]/v[n], {n, 1, z}] (* A203688 *)
%Y A203687 Cf. A203685, A203688, A203689.
%K A203687 nonn,easy
%O A203687 1,2
%A A203687 _Clark Kimberling_, Jan 04 2012
%E A203687 Definition corrected by _Georg Fischer_, Nov 25 2021