A203675 Vandermonde sequence using x^2 - xy + y^2 applied to (1,4,9,...,n^2).

1, 13, 57889, 560058939856, 42130404012097952586256, 65111467563626175389271488157658681344, 4528499444374253250530486688998183592108605307719698157568

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Crossrefs

Cf. A203673, A367668.

Programs

Mathematica

f[j_] := j^2; z = 12;
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}]          (* A203675 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203676 *)

Formula

a(n) ~ c * (2 + sqrt(3))^(sqrt(3)*n*(n+1)/2) * n^(2*n^2 - 2*n - 3/2) / exp(3*n^2 - Pi*n*(n+1)/4 - 2*n), where c = 0.07463795295314976973866568785704370572893158254239607676544741150586459722... - Vaclav Kotesovec, Nov 25 2023