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 A203689 Vandermonde sequence using x^2 + y^2 applied to (1,2,6,...,n!). 4
 1, 5, 7400, 1515608208000, 67968144879431450715389952000, 2618461740951506934762583974466059060153960058218086400000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A093883 for a discussion and guide to related sequences. LINKS Table of n, a(n) for n=1..6. FORMULA a(n) ~ c * n^(2*n^3/3 + n^2/2 - 7*n/6 - 3/4) * (2*Pi)^(n*(n-1)/2) / exp(8*n^3/9 - n^2/4 - 2*n), where c = 0.574053995428296820717722993471497472923951255369819486673614046900594637219... - Vaclav Kotesovec, Nov 21 2023 MATHEMATICA f[j_] := j!; z = 8; 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}] (* A203689 *) Table[v[n + 1]/v[n], {n, 1, z}] (* A203690 *) CROSSREFS Sequence in context: A292334 A202156 A117711 * A116140 A243235 A145530 Adjacent sequences: A203686 A203687 A203688 * A203690 A203691 A203692 KEYWORD nonn AUTHOR Clark Kimberling, Jan 04 2012 STATUS approved

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Last modified April 24 18:17 EDT 2024. Contains 371962 sequences. (Running on oeis4.)