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A203589
Vandermonde sequence using x^2 + y^2 applied to (1,3,5,...,2n-1).
3
1, 10, 8840, 1897064000, 192924579369600000, 15340654595434137315840000000, 1423341281300698059502838358528000000000000, 215088732628531399592688671811428988579913728000000000000000
OFFSET
1,2
COMMENTS
See A093883 for a discussion and guide to related sequences.
FORMULA
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
MATHEMATICA
f[j_] := 2 j - 1; z = 12;
v[n_] := Product[Product[f[j]^2 + f[k]^2, {j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203589 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203590 *)
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 *)
CROSSREFS
Sequence in context: A229152 A125543 A291562 * A109893 A208781 A125544
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 04 2012
STATUS
approved