A285021 - OEIS

%I #20 Mar 11 2024 01:50:33

%S 1,10,200,400,16000,800000,16000000,160000000,2560000000,25600000000,

%T 2560000000000,25600000000000,1024000000000000,409600000000000,

%U 8192000000000000,409600000000000000,65536000000000000000,655360000000000000000,2621440000000000000000,26214400000000000000000,5242880000000000000000000,52428800000000000000000000

%N Denominator of binomial(2*n,n)/20^n.

%H Chai Wah Wu, <a href="/A285021/b285021.txt">Table of n, a(n) for n = 0..769</a>

%F A285020(n)/a(n) = (-1/5)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).

%F Sum_{k>=0} A285020(k)/a(k) = sqrt(5)/2.

%F Sum_{k>=0} (-1)^k*A285020(k)/a(k) = sqrt(5/6).

%F Sum_{k>=0} (-1)^(k+1)*A285020(k)/a(k) = -sqrt(5/6).

%t Denominator[Table[(-1/5)^n*Sqrt[Pi]/(Gamma[1/2-n]*Gamma[1+n]),{n,0,25}]]

%Y Cf. A285020 (numerators).

%K nonn,frac

%O 0,2

%A _Ralf Steiner_, Apr 08 2017