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

Terms

a(0) =1a(1) =1a(2) =5a(3) =13a(4) =43a(5) =131a(6) =411a(7) =1275a(8) =3963a(9) =12283a(10) =38023a(11) =117503a(12) =362605a(13) =1117429a(14) =3439229a(15) =10572957a(16) =32468787a(17) =99610515a(18) =305313711a(19) =935015271a(20) =2861204529a(21) =8749050009a(22) =26734768305a(23) =81642292977a(24) =249169635477a(25) =760033085301