A100561 Denominator of Sum_{k=0..[n/2]} 1/binomial(n,k).
1, 1, 2, 3, 12, 10, 60, 105, 140, 63, 280, 1155, 27720, 25740, 8008, 9009, 16380, 17017, 6126120, 2909907, 5542680, 2645370, 232792560, 111546435, 535422888, 128707425, 2974571600, 717084225, 80313433200, 77636318760, 2329089562800, 4512611027925, 546983154900
Offset: 0
Examples
1, 3/2, 4/3, 17/12, 13/10, 77/60, 128/105, 167/140, 73/63, 319/280, 1294/1155, 30697/27720, 28211/25740, 8707/8008, 9728/9009, 17587/16380, 18181/17017, ... = A100560/A100561
Programs
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Mathematica
Denominator[Table[Sum[1/Binomial[n,k],{k,0,Floor[n/2]}],{n,0,40}]] (* Harvey P. Dale, Dec 24 2014 *)