a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026637.

Terms

a(0) =1a(1) =4a(2) =24a(3) =90a(4) =365a(5) =1376a(6) =5272a(7) =20098a(8) =77016a(9) =295836a(10) =1139834a(11) =4402490a(12) =17042341a(13) =66101848a(14) =256838544a(15) =999512058a(16) =3895191476a(17) =15199297796a(18) =59377405654a(19) =232208188726a(20) =908978576496