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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. 3

%I #37 Jan 15 2017 13:21:23

%S 2,16,384,6144,819200,19660800,7707033600,3288334336,14205604331520,

%T 568224173260800,3741775508275200,179605224397209600,

%U 135982707495615332352,1410191040695270113280,169222924883432413593600,10830267192539674469990400,1655509272671188586751590400

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

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

%t 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]

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

%K nonn,frac

%O 0,1

%A _Ralf Steiner_, Jan 14 2017

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Last modified February 28 07:05 EST 2024. Contains 370387 sequences. (Running on oeis4.)