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Numerator of 2*Sum(C(n,w)/w,w=1..n/2-1)+C(n,n/2)/(n/2) if n is even otherwise of 2*Sum(C(n,w)/w,w=1..(n-1)/2).
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%I #4 Mar 30 2012 16:49:45

%S 2,6,11,20,101,175,593,173,1502,2684,28649,52169,662393,1224077,

%T 4506259,4210067,23506871,44294491,41572193,78849257,1639049932,

%U 3125022742,23750582143,9095291663,225666905951,144544431373,276913262539,76244134117,732674442397

%N Numerator of 2*Sum(C(n,w)/w,w=1..n/2-1)+C(n,n/2)/(n/2) if n is even otherwise of 2*Sum(C(n,w)/w,w=1..(n-1)/2).

%e 2, 6, 11, 20, 101/3, 175/3, 593/6, 173, 1502/5, 2684/5, 28649/30, ...

%p b := binomial; f3 := n->if n mod 2 = 0 then 2*add(b(n,w)/w,w=1..n/2-1)+b(n,n/2)/(n/2); else 2*add(b(n,w)/w,w=1..(n-1)/2); fi;

%Y Cf. A085568-A086673.

%K nonn,frac

%O 2,1

%A _N. J. A. Sloane_, Jul 07 2003