A203677 - OEIS

A203677

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

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

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OFFSET

1,2

COMMENTS

See A093883 for a discussion and guide to related sequences.

LINKS

Table of n, a(n) for n=1..7.

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

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 *)

CROSSREFS

Cf. A324437.

Sequence in context: A046883 A046884 A269442 * A099499 A051157 A177918

Adjacent sequences: A203674 A203675 A203676 * A203678 A203679 A203680

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 04 2012

STATUS

approved