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

Terms

a(0) =1a(1) =0a(2) =2a(3) =3a(4) =10a(5) =30a(6) =77a(7) =252a(8) =690a(9) =2145a(10) =6292a(11) =19019a(12) =57421a(13) =173264a(14) =527340a(15) =1600788a(16) =4885698a(17) =14911941a(18) =45623237a(19) =139763525a(20) =428688260a(21) =1316652480a(22) =4047752865a(23) =12457365570a(24) =38371634925a(25) =118295112780a(26) =364968310176