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

%I #12 Nov 26 2023 04:07:46

%S 1,13,57889,560058939856,42130404012097952586256,

%T 65111467563626175389271488157658681344,

%U 4528499444374253250530486688998183592108605307719698157568

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

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

%F 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

%t f[j_] := j^2; z = 12;

%t u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2, {j, 1, k - 1}]

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

%t Table[v[n], {n, 1, z}] (* A203675 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203676 *)

%Y Cf. A203673, A367668.

%K nonn,changed

%O 1,2

%A _Clark Kimberling_, Jan 04 2012

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Last modified November 29 12:41 EST 2023. Contains 367445 sequences. (Running on oeis4.)