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%I #22 Mar 11 2024 01:49:40
%S 1,4,576,4608,16588800,66355200,104044953600,1664719257600,
%T 16441671680000,5327101624320000,92819418702151680000,
%U 742555349617213440000,98385613602882311946240000,131180818137176415928320000,1199367480111327231344640000,29850923949437477757911040000,12196892137874302548391671889920000
%N a(n) is the denominator of Sum_{m=0..n}(Sum_{k=0..m} ((k+1)/(m-k+1)^2) * (Catalan(k)/(2^(2*k)))^2)*(Sum_{k=0..n-m} ((k+1)/(n-m-k+1)^2) * (Catalan(k)/(2^(2*k)))^2).
%C The series A282195(n)/a(n) is absolutely convergent to (2/3 Pi)^2.
%H Paolo P. Lava, <a href="/A282196/b282196.txt">Table of n, a(n) for n = 0..100</a>
%t b[n_]=(Sum[((k+1)/(n-k+1)^2)((CatalanNumber[k])/(2^(2k)))^2, {k, 0, n}]); a[n_] = Sum[(b[k]*b[n - k]), {k, 0, n}]; Denominator /@a/@ Range[0, 10]
%o (PARI) C(n) = binomial(2*n,n)/(n+1);
%o b(n) = sum(k=0, n, ((k+1)/(n-k+1)^2) * (C(k)/(2^(2*k)))^2);
%o a(n) = denominator(sum(k=0, n, b(k)*b(n-k))); \\ _Michel Marcus_, Feb 11 2017
%Y Cf. A281070, A280723, A000108 (Catalan), A282195 (numerators)
%K nonn,frac
%O 0,2
%A _Ralf Steiner_, Feb 08 2017
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