A281070 a(n) is the numerator of 6 * Sum_{k=0..n} ((k+1)/(n-k+1)^2) * (Catalan(k)/(2^(2*k+1)))^2.

3, 9, 109, 1037, 91027, 1540981, 447810157, 147053171, 503445581741, 16337573574319, 88973047698967, 3588920671411951, 2314594755016141847, 20685050199210758743, 2160689714871889935101, 121435710295138581181033, 16427863327419202412927713

Offset: 0

Author

Ralf Steiner, Jan 14 2017

Keywords

• nonn
• frac

Comments

The series a(n)/A280723(n) is absolutely convergent to Pi.

Crossrefs

Cf. A000108 (Catalan), A280723 (denominators).

Programs

Mathematica

a[n_]=6(Sum[(1/(n-k+1)^2)((CatalanNumber[k])/(2^(2k+1)))^2(k+1),{k,0, n}]); Numerator /@a/@ Range[0,10]