a(n) = T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027082.

Terms

a(0) =1a(1) =5a(2) =16a(3) =50a(4) =152a(5) =452a(6) =1331a(7) =3897a(8) =11378a(9) =33186a(10) =96791a(11) =282461a(12) =825013a(13) =2412157a(14) =7060154a(15) =20686324a(16) =60673102a(17) =178126774a(18) =523426827a(19) =1539393889a(20) =4530901919a(21) =13345545959a(22) =39335284312a(23) =116011722730a(24) =342354698603