LINKS
G. C. Greubel, <a href="/A203476/b203476_1.txt">Table of n, a(n) for n = 1..200</a>
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G. C. Greubel, <a href="/A203476/b203476_1.txt">Table of n, a(n) for n = 1..200</a>
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a(n) = v(n+1)/v(n), where v = A203475.
G. C. Greubel, <a href="/A203476/b203476_1.txt">Table of n, a(n) for n = 1..200</a>
a(n) = Product_{j=1..n} ((n+1)^2 + j^2). - G. C. Greubel, Aug 28 2023
(* First program *)
f[j_] := j^2; z = 15;
v[n_] := Product[Product[f[k] + f[j], {j, k-1}], {k, 2, n}]
{j, 1, k - 1}], {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203475 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203476 *)
(* Second program *)
Table[Product[j^2 +(n+1)^2 , {j, n}], {n, 20}] (* G. C. Greubel, Aug 28 2023 *)
(Magma) [(&*[(n+1)^2 + j^2: j in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 28 2023
(SageMath) [product(j^2+(n+1)^2 for j in range(1, n+1)) for n in range(1, 21)] # G. C. Greubel, Aug 28 2023
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a(n) ~ 2^(n + 1/2) * exp(Pi*(n+1)/2 - 2*n) * n^(2*n). - Vaclav Kotesovec, Jan 25 2019
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_Clark Kimberling (ck6(AT)evansville.edu), _, Jan 02 2012