A280723 a(n) is the denominator of 6 * Sum_{k=0..n} ((k+1)/(n-k+1)^2) * (Catalan(k)/(2^(2*k+1)))^2.

2, 16, 384, 6144, 819200, 19660800, 7707033600, 3288334336, 14205604331520, 568224173260800, 3741775508275200, 179605224397209600, 135982707495615332352, 1410191040695270113280, 169222924883432413593600, 10830267192539674469990400, 1655509272671188586751590400

Offset: 0

Author

Ralf Steiner, Jan 14 2017

Keywords

• nonn
• frac

Comments

The series A281070(n)/a(n) is absolutely convergent to Pi.

Crossrefs

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

Programs

Mathematica

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