A087940 a(n)=sum(k=0,n,binomial(n+(-1)^k,k)).

1, 5, 9, 20, 39, 80, 159, 320, 639, 1280, 2559, 5120, 10239, 20480, 40959, 81920, 163839, 327680, 655359, 1310720, 2621439, 5242880, 10485759, 20971520, 41943039, 83886080, 167772159, 335544320, 671088639, 1342177280, 2684354559