A203476 a(n) = v(n+1)/v(n), where v = A203475.

5, 130, 8500, 1051076, 211255200, 62840245000, 25959932960000, 14224928867370000, 9986120745657472000, 8740787543400204500000, 9333385482079885824000000, 11942338721669302523305000000, 18038821394494464638896640000000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A093883, A110468, A203475.

Programs

Magma

[(&*[(n+1)^2 + j^2: j in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 28 2023

Mathematica

(* First program *)
f[j_]:= j^2; z = 15;
v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]
Table[v[n], {n,z}]           (* A203475 *)
Table[v[n+1]/v[n], {n,z-1}]  (* A203476 *)
(* Second program *)
Table[Product[j^2 +(n+1)^2 , {j,n}], {n,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

Formula

a(n) ~ 2^(n + 1/2) * exp(Pi*(n+1)/2 - 2*n) * n^(2*n). - Vaclav Kotesovec, Jan 25 2019

a(n) = Product_{j=1..n} ((n+1)^2 + j^2). - G. C. Greubel, Aug 28 2023