A203677 Vandermonde sequence using x^2 + y^2 applied to (1,4,9,...,n^2).

1, 17, 135218, 3185418047264, 795022479172023183220864, 5554004683279652358469137440150614769664, 2378852972988348412358457063032448409092378064835941488918528

Offset: 1

Author

Clark Kimberling, Jan 04 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Crossrefs

Cf. A324437.

Programs

Mathematica

f[j_] := j^2; z = 12;
u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203677 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203678 *)

Formula

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