cp's OEIS Frontend

A203589 Vandermonde sequence using x^2 + y^2 applied to (1,3,5,...,2n-1).

%I A203589 #12 Sep 08 2023 04:47:36
%S A203589 1,10,8840,1897064000,192924579369600000,
%T A203589 15340654595434137315840000000,
%U A203589 1423341281300698059502838358528000000000000,215088732628531399592688671811428988579913728000000000000000
%N A203589 Vandermonde sequence using x^2 + y^2 applied to (1,3,5,...,2n-1).
%C A203589 See A093883 for a discussion and guide to related sequences.
%F A203589 a(n) ~ 2^(3*n^2/2 - 3*n/2 - 3/8) * n^(n*(n-1)) / exp((6 - Pi)*n^2/4 - n + Pi/48). - _Vaclav Kotesovec_, Sep 08 2023
%t A203589 f[j_] := 2 j - 1; z = 12;
%t A203589 v[n_] := Product[Product[f[j]^2 + f[k]^2, {j, 1, k - 1}], {k, 2, n}]
%t A203589 Table[v[n], {n, 1, z}]          (* A203589 *)
%t A203589 Table[v[n + 1]/v[n], {n, 1, z}] (* A203590 *)
%t A203589 Table[Product[(2*k - 1)^2 + (2*j - 1)^2, {k, 1, n}, {j, 1, k-1}], {n, 1, 10}] (* _Vaclav Kotesovec_, Sep 08 2023 *)
%Y A203589 Cf. A293290, A324403.
%K A203589 nonn
%O A203589 1,2
%A A203589 _Clark Kimberling_, Jan 04 2012