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A203691 Vandermonde sequence using x^2 + xy + y^2 applied to the first n triangular numbers: 1,3,6,10,...,n(n+1)/2.

%I A203691 #8 Jan 14 2013 07:53:35
%S A203691 1,13,35217,106499166228,1193900625351298928700,
%T A203691 125977443935710401573828500229372900,
%U A203691 267622663746762354024098339277838006317831656007585600
%N A203691 Vandermonde sequence using x^2 + xy + y^2 applied to the first n triangular numbers: 1,3,6,10,...,n(n+1)/2.
%C A203691 See A093883 for a discussion and guide to related sequences.
%t A203691 f[j_] := j (j + 1)/2; z = 11;
%t A203691 u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
%t A203691   {j, 1, k - 1}]
%t A203691 v[n_] := Product[u[n], {k, 2, n}]
%t A203691 Table[v[n], {n, 1, z}]          (* A203691 *)
%t A203691 Table[v[n + 1]/v[n], {n, 1, z}] (* A203692 *)
%K A203691 nonn
%O A203691 1,2
%A A203691 _Clark Kimberling_, Jan 04 2012