A100560 Numerator of Sum_{k=0..[n/2]} 1/binomial(n,k).
1, 1, 3, 4, 17, 13, 77, 128, 167, 73, 319, 1294, 30697, 28211, 8707, 9728, 17587, 18181, 6517513, 3084316, 5855671, 2786599, 244579999, 116918176, 560006983, 134354573, 3099540819, 745984697, 83423830027, 80530073893, 2412760934249, 4669066440704, 565308230449
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