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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. 3

%I

%S 1,13,35217,106499166228,1193900625351298928700,

%T 125977443935710401573828500229372900,

%U 267622663746762354024098339277838006317831656007585600

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

%C See A093883 for a discussion and guide to related sequences.

%t f[j_] := j (j + 1)/2; z = 11;

%t u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,

%t {j, 1, k - 1}]

%t v[n_] := Product[u[n], {k, 2, n}]

%t Table[v[n], {n, 1, z}] (* A203691 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203692 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 04 2012

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Last modified February 3 18:43 EST 2023. Contains 360044 sequences. (Running on oeis4.)