a(n) = Sum_{k=0..n} binomial(n+(-1)^k, k).

Terms

a(0) =1a(1) =5a(2) =9a(3) =20a(4) =39a(5) =80a(6) =159a(7) =320a(8) =639a(9) =1280a(10) =2559a(11) =5120a(12) =10239a(13) =20480a(14) =40959a(15) =81920a(16) =163839a(17) =327680a(18) =655359a(19) =1310720a(20) =2621439a(21) =5242880a(22) =10485759a(23) =20971520a(24) =41943039a(25) =83886080a(26) =167772159a(27) =335544320a(28) =671088639a(29) =1342177280