a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027082.

Terms

a(0) =1a(1) =5a(2) =16a(3) =68a(4) =276a(5) =1084a(6) =4227a(7) =16207a(8) =61348a(9) =229888a(10) =853737a(11) =3146649a(12) =11522891a(13) =41959547a(14) =152044236a(15) =548575204a(16) =1971713228a(17) =7062750256a(18) =25222033633a(19) =89824310345a(20) =319101174069