cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A203678 v(n+1)/v(n), where v=A203677.

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%I A203678 #10 Sep 08 2023 06:29:57
%S A203678 17,7954,23557648,249581834276,6985971879768576,428313101742584476552,
%T A203678 50648802606721926260916224,10537561069087080809570265074448,
%U A203678 3598422455223499123258044906373120000,1910287477970606754101128649923632473220896
%N A203678 v(n+1)/v(n), where v=A203677.
%C A203678 See A093883 for a discussion and guide to related sequences.
%F A203678 a(n) ~ 2^(n + 1/2) * (1 + sqrt(2))^(sqrt(2)*(n+1)) * exp((n+1)*Pi/sqrt(2) - 4*n) * n^(4*n). - _Vaclav Kotesovec_, Sep 08 2023
%t A203678 f[j_] := j^2; z = 12;
%t A203678 u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
%t A203678 v[n_] := Product[u[n], {k, 2, n}]
%t A203678 Table[v[n], {n, 1, z}]          (* A203677 *)
%t A203678 Table[v[n + 1]/v[n], {n, 1, z}] (* A203678 *)
%t A203678 Table[Product[k^4 + (n + 1)^4, {k, 1, n}], {n, 1, 12}] (* _Vaclav Kotesovec_, Sep 08 2023 *)
%K A203678 nonn
%O A203678 1,1
%A A203678 _Clark Kimberling_, Jan 04 2012