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A085569
Denominator of 2*Sum(C(n,w)/(2*w+1),w=0..n/2-1)+C(n,n/2)/(n+1) if n is even, or of 2*Sum(C(n,w)/(2*w+1),w=0..(n-1)/2) if n is odd.
1
1, 1, 3, 1, 15, 3, 7, 15, 45, 5, 231, 21, 455, 315, 45, 3, 1683, 3465, 7315, 5005, 3003, 143, 13455, 585, 6825, 13923, 3213, 6545, 515185, 17765, 110143, 31977, 2078505, 62985, 1789515, 51129, 210197, 426075, 246675, 6325, 1400355, 34155, 41612175, 84192075
OFFSET
0,3
EXAMPLE
1, 2, 8/3, 4, 88/15, 28/3, 104/7, 376/15, 1904/45, 372/5, 30152/231, ...
MAPLE
b := binomial; f1 := n->if n mod 2 = 0 then 2*add(b(n, w)/(2*w+1), w=0..n/2-1)+b(n, n/2)/(n+1); else 2*add(b(n, w)/(2*w+1), w=0..(n-1)/2); fi;
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jul 07 2003
STATUS
approved