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%I #13 Sep 25 2020 04:26:27
%S 0,1,34,55511,11575291716,548347875819272649,
%T 8811385079228718926321932614,
%U 66303398534111438173105653188803948359375,308529654991526005900670429792887300937160115962403125000
%N a(n) = ((2*n+1)!!)^n * (Sum_{k=1..n} 1/(2*k+1)^n).
%F a(n) ~ 2^(n*(n + 3/2)) * n^(n*(n+1)) / (3^n * exp(n^2 - 11/24)). - _Vaclav Kotesovec_, Sep 25 2020
%t Table[((2*n + 1)!!)^n * Sum[1/(2*k + 1)^n, {k, 1, n}], {n, 0, 10}] (* _Vaclav Kotesovec_, Sep 25 2020 *)
%o (PARI) {a(n) = prod(k=1, n, 2*k+1)^n*sum(k=1, n, 1/(2*k+1)^n)}
%Y Main diagonal of A335095.
%Y Cf. A291676.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 12 2020
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