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%I #11 Jun 04 2022 21:51:06
%S 1,2,8,120,672,5600,79200,50450400,201801600,10291881600,17776886400,
%T 2151003254400,3805621142400,643149973065600,643149973065600,
%U 31085582031504000,226741892465088000,65528406922410432000,31039771700089152000,414598230598090803264000,16583929223923632130560
%N Denominator of 3*Sum_{i=1..n} 1/(i^2*C(2*i,i)).
%H C. Elsner, <a href="http://www.fq.math.ca/Papers1/43-1/paper43-1-5.pdf">On recurrence formulas for sums involving binomial coefficients</a>, Fib. Q., 43,1 (2005), 31-45.
%F 3*Sum_{i >= 1} 1/(i^2*C(2*i, i)) = zeta(2) = Pi^2/6.
%e 0, 3/2, 13/8, 197/120, 1105/672, 9211/5600, 130277/79200, 82987349/50450400, ... -> Pi^2/6.
%o (PARI) a(n) = denominator(3*sum(i=1, n, 1/(i^2*binomial(2*i, i)))); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A112093.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 30 2005
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