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

1, 7, 5859, 3201146676, 3820181459144204700, 25381616622722369500521817413900, 2012800150183968180465350145758736863679028900800, 3623820214658807704726540455788270697258988626189027049678195383091200

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}]          (* A203693 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203694 *)