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

%I #10 Sep 08 2023 09:06:01

%S 1,17,135218,3185418047264,795022479172023183220864,

%T 5554004683279652358469137440150614769664,

%U 2378852972988348412358457063032448409092378064835941488918528

%N Vandermonde sequence using x^2 + 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^(n^2/2 - 1) * (1 + sqrt(2))^(n*(n+1)/sqrt(2)) * exp((Pi/2^(3/2) - 3)*n^2 + (Pi/2^(3/2) + 2)*n) * n^(2*n^2 - 2*n - 3/2), where c = 0.154147406559582639039828423669556073435424655001221440918550218582474208... - _Vaclav Kotesovec_, Sep 08 2023

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

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

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

%t Table[v[n], {n, 1, z}] (* A203677 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203678 *)

%Y Cf. A324437.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 04 2012