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

1,1

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A093883, A110468, A203475.

Sequence in context: A332317 A069078 A003732 * A203702 A142892 A229879

Adjacent sequences: A203473 A203474 A203475 * A203477 A203478 A203479

Keyword

nonn

Author

Clark Kimberling, Jan 02 2012

Status

approved