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%I #11 Nov 21 2023 06:03:57
%S 10,1665,1497224,4485885300,34184139841800,557745681594010000,
%T 17295475176752223859200,934164847784800073360250000,
%U 82223581117536608232019062500000,11191248877703366469751902789287961600
%N v(n+1)/v(n), where v=A203695.
%C See A093883 for a discussion and guide to related sequences.
%F a(n) ~ (1 + sqrt(2))^((2*n+3)/sqrt(2)) * exp(Pi*(2*n+3)/(2*sqrt(2)) - 4*n) * n^(4*n) / 2^(n-1). - _Vaclav Kotesovec_, Nov 21 2023
%t f[j_] := j (j + 1)/2; z = 11;
%t u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
%t v[n_] := Product[u[n], {k, 2, n}]
%t Table[v[n], {n, 1, z}] (* A203695 *)
%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203696 *)
%t Table[Product[k^2*(k+1)^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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