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

1, 13, 35217, 106499166228, 1193900625351298928700, 125977443935710401573828500229372900, 267622663746762354024098339277838006317831656007585600

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Programs

Mathematica

f[j_] := j (j + 1)/2; z = 11;
u[n_] := Product[f[j]^2 + f[j] f[k] + f[k]^2,
  {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203691 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203692 *)