a(n) = Sum_{k=0..n-1} T(n,k)*T(n,2n-k), T given by A027960.

Terms

a(0) =1a(1) =13a(2) =48a(3) =176a(4) =580a(5) =1844a(6) =5667a(7) =17047a(8) =50404a(9) =147090a(10) =424686a(11) =1215528a(12) =3453733a(13) =9752641a(14) =27393240a(15) =76587284a(16) =213260152a(17) =591707612a(18) =1636514439a(19) =4513276555a(20) =12414985996a(21) =34071252918a(22) =93305816418a(23) =255027755856a(24) =695815086025