a(n) = Sum_{k=0..n} binomial(k-1,2*k-1-n)*binomial(k,2*k-n), with a(0) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =16a(6) =39a(7) =95a(8) =233a(9) =577a(10) =1436a(11) =3590a(12) =9011a(13) =22691a(14) =57299a(15) =145043a(16) =367931a(17) =935078a(18) =2380405a(19) =6068745a(20) =15492702a(21) =39598631a(22) =101323446a(23) =259522398a(24) =665332007a(25) =1707137941a(26) =4383662419a(27) =11264675925a(28) =28966161253a(29) =74530441162