a(n) = Sum_{k=0..n-2} T(n,k)*T(n,k+2), T given by A026736.

Terms

a(0) =1a(1) =6a(2) =32a(3) =136a(4) =640a(5) =2593a(6) =11860a(7) =47532a(8) =215531a(9) =861334a(10) =3893621a(11) =15549166a(12) =70199065a(13) =280316029a(14) =1264697307a(15) =5050617474a(16) =22776900816a(17) =90972831448a(18) =410117333080