a(n) = Sum_{k=0..n-1} T(n,k)*T(n,k+1), T given by A026736.

Terms

a(0) =1a(1) =4a(2) =15a(3) =63a(4) =237a(5) =1034a(6) =3945a(7) =17577a(8) =67640a(9) =304902a(10) =1179415a(11) =5352038a(12) =20771331a(13) =94628132a(14) =368083879a(15) =1680820301a(16) =6548692260a(17) =29946087674a(18) =116816782997a(19) =534628747310