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A203694 v(n+1)/v(n), where v=A203693. 2

%I #10 Nov 21 2023 08:18:10

%S 7,837,546364,1193379075,6644086647237,79301495255509072,

%T 1800387492184752516864,71233673448265142887288125,

%U 4594697931876986561881103171875,458419756376283291989575799311713024

%N v(n+1)/v(n), where v=A203693.

%C See A093883 for a discussion and guide to related sequences.

%F a(n) ~ (2 + sqrt(3))^(sqrt(3)*(2*n+3)/2) * exp((Pi/2 - 4)*n + 3*Pi/4) * n^(4*n) / 2^(2*n). - _Vaclav Kotesovec_, Nov 21 2023

%t f[j_] := j (j + 1)/2; z = 11;

%t u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2,

%t {j, 1, k - 1}]

%t v[n_] := Product[u[n], {k, 2, n}]

%t Table[v[n], {n, 1, z}] (* A203693 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203694 *)

%t Table[Product[k^2*(k + 1)^2/4 - k*(k + 1)*(n + 1)*(n + 2)/4 + (n + 1)^2*(n + 2)^2/4, {k, 1, n}], {n, 1, 10}] (* _Vaclav Kotesovec_, Nov 21 2023 *)

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 04 2012

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Last modified July 25 03:05 EDT 2024. Contains 374586 sequences. (Running on oeis4.)