A085568
Numerator 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.
Original entry on oeis.org
1, 2, 8, 4, 88, 28, 104, 376, 1904, 372, 30152, 4952, 193072, 245848, 64304, 7984, 8303392, 32131172, 126932136, 164384184, 185914544, 16850280, 3006076208, 249890288, 5554299808, 21745428728, 9598969456, 37645191344, 5687521456416, 378608431568, 4518712438048
Offset: 0
1, 2, 8/3, 4, 88/15, 28/3, 104/7, 376/15, 1904/45, 372/5, 30152/231, ...
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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;
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.
Original entry on oeis.org
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
1, 2, 8/3, 4, 88/15, 28/3, 104/7, 376/15, 1904/45, 372/5, 30152/231, ...
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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;
A085570
If n mod 2 = 0 then 2*Sum(floor(C(n,w)/(2*w+1)),w=0..n/2-1)+floor(C(n,n/2)/(n+1)) otherwise 2*Sum(floor(C(n,w)/(2*w+1)),w=0..(n-1)/2).
Original entry on oeis.org
1, 2, 2, 4, 5, 8, 14, 24, 39, 74, 128, 232, 423, 776, 1426, 2660, 4931, 9268, 17346, 32840, 61903, 117832, 223410, 427156, 813812, 1561830, 2987535, 5751742, 11039759, 21312036, 41025866, 79386066, 153208323, 297072312, 574604611, 1116186954, 2163216427
Offset: 0
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b := binomial; f2 := n->if n mod 2 = 0 then 2*add(floor(b(n,w)/(2*w+1)),w=0..n/2-1)+floor(b(n,n/2)/(n+1)); else 2*add(floor(b(n,w)/(2*w+1)),w=0..(n-1)/2); fi;
A085571
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).
Original entry on oeis.org
2, 6, 11, 20, 101, 175, 593, 173, 1502, 2684, 28649, 52169, 662393, 1224077, 4506259, 4210067, 23506871, 44294491, 41572193, 78849257, 1639049932, 3125022742, 23750582143, 9095291663, 225666905951, 144544431373, 276913262539, 76244134117, 732674442397
Offset: 2
2, 6, 11, 20, 101/3, 175/3, 593/6, 173, 1502/5, 2684/5, 28649/30, ...
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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;
A085572
Denominator 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).
Original entry on oeis.org
1, 1, 1, 1, 3, 3, 6, 1, 5, 5, 30, 30, 210, 210, 420, 210, 630, 630, 315, 315, 3465, 3465, 13860, 2772, 36036, 12012, 12012, 1716, 8580, 8580, 17160, 8580, 145860, 204204, 612612, 612612, 11639628, 11639628, 29099070, 29099070, 29099070, 29099070, 1322685, 14549535
Offset: 2
2, 6, 11, 20, 101/3, 175/3, 593/6, 173, 1502/5, 2684/5, 28649/30, ...
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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;
Showing 1-5 of 5 results.