OFFSET
0,2
COMMENTS
The series a(n)/A282196(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}]; Numerator /@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) = numerator(sum(k=0, n, b(k)*b(n-k))); \\ Michel Marcus, Feb 11 2017
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ralf Steiner, Feb 08 2017
STATUS
approved