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A203693 Vandermonde sequence using x^2 - xy + y^2 applied to the first n triangular numbers: 1,3,6,10,...,n(n+1)/2.

%I A203693 #8 Jan 14 2013 07:54:21
%S A203693 1,7,5859,3201146676,3820181459144204700,
%T A203693 25381616622722369500521817413900,
%U A203693 2012800150183968180465350145758736863679028900800,3623820214658807704726540455788270697258988626189027049678195383091200
%N A203693 Vandermonde sequence using x^2 - xy + y^2 applied to the first n triangular numbers: 1,3,6,10,...,n(n+1)/2.
%C A203693 See A093883 for a discussion and guide to related sequences.
%t A203693 f[j_] := j (j + 1)/2; z = 11;
%t A203693 u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2,
%t A203693   {j, 1, k - 1}]
%t A203693 v[n_] := Product[u[n], {k, 2, n}]
%t A203693 Table[v[n], {n, 1, z}]          (* A203693 *)
%t A203693 Table[v[n + 1]/v[n], {n, 1, z}] (* A203694 *)
%K A203693 nonn
%O A203693 1,2
%A A203693 _Clark Kimberling_, Jan 04 2012