A203476 - OEIS

%I #16 Aug 28 2023 03:08:28

%S 5,130,8500,1051076,211255200,62840245000,25959932960000,

%T 14224928867370000,9986120745657472000,8740787543400204500000,

%U 9333385482079885824000000,11942338721669302523305000000,18038821394494464638896640000000

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

%H G. C. Greubel, <a href="/A203476/b203476.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) ~ 2^(n + 1/2) * exp(Pi*(n+1)/2 - 2*n) * n^(2*n). - _Vaclav Kotesovec_, Jan 25 2019

%F a(n) = Product_{j=1..n} ((n+1)^2 + j^2). - _G. C. Greubel_, Aug 28 2023

%t (* First program *)

%t f[j_]:= j^2; z = 15;

%t v[n_]:= Product[Product[f[k] + f[j], {j,k-1}], {k,2,n}]

%t Table[v[n], {n,z}]           (* A203475 *)

%t Table[v[n+1]/v[n], {n,z-1}]  (* A203476 *)

%t (* Second program *)

%t Table[Product[j^2 +(n+1)^2 , {j,n}], {n,20}] (* _G. C. Greubel_, Aug 28 2023 *)

%o (Magma) [(&*[(n+1)^2 + j^2: j in [1..n]]): n in [1..20]]; // _G. C. Greubel_, Aug 28 2023

%o (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

%Y Cf. A093883, A110468, A203475.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 02 2012