a(n) = T(n,m) + T(n,m+1) + ... + T(n,n), m=[ (n+1)/2 ], T given by A026780.

Terms

a(0) =1a(1) =1a(2) =4a(3) =5a(4) =18a(5) =24a(6) =84a(7) =115a(8) =400a(9) =554a(10) =1934a(11) =2690a(12) =9474a(13) =13180a(14) =46962a(15) =65193a(16) =235338a(17) =325568a(18) =1191292a(19) =1641192a(20) =6086880a(21) =8348342a(22) =31369180a(23) =42831204a(24) =162943236a(25) =221515918a(26) =852512496a(27) =1154208486a(28) =4489722568a(29) =6055426942