A282196 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).

1, 4, 576, 4608, 16588800, 66355200, 104044953600, 1664719257600, 16441671680000, 5327101624320000, 92819418702151680000, 742555349617213440000, 98385613602882311946240000, 131180818137176415928320000, 1199367480111327231344640000, 29850923949437477757911040000, 12196892137874302548391671889920000

Offset

0,2

Comments

The series A282195(n)/a(n) is absolutely convergent to (2/3 Pi)^2.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..100

Mathematica

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]

Prog

(PARI) C(n) = binomial(2*n, n)/(n+1);
b(n) = sum(k=0, n, ((k+1)/(n-k+1)^2) * (C(k)/(2^(2*k)))^2);
a(n) = denominator(sum(k=0, n, b(k)*b(n-k))); \\ Michel Marcus, Feb 11 2017

Crossrefs

Cf. A281070, A280723, A000108 (Catalan), A282195 (numerators)

Sequence in context: A267066 A159530 A274470 * A114764 A134372 A177926

Adjacent sequences: A282193 A282194 A282195 * A282197 A282198 A282199

Keyword

nonn,frac

Author

Ralf Steiner, Feb 08 2017

Status

approved