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

Terms

a(0) =1a(1) =2a(2) =5a(3) =22a(4) =68a(5) =206a(6) =631a(7) =1870a(8) =5467a(9) =15836a(10) =45416a(11) =129260a(12) =365565a(13) =1028122a(14) =2877697a(15) =8021010a(16) =22274476a(17) =61653850a(18) =170152275a(19) =468347046a(20) =1286055927a(21) =3523777912a(22) =9635982160a(23) =26302324504a(24) =71674754873a(25) =195015074610a(26) =529846108989