a(n) = Sum_{k=0..2n} (k+1) * A027052(n, 2n-k).

Terms

a(0) =1a(1) =4a(2) =13a(3) =38a(4) =111a(5) =326a(6) =961a(7) =2842a(8) =8425a(9) =25020a(10) =74403a(11) =221488a(12) =659895a(13) =1967422a(14) =5869055a(15) =17516540a(16) =52300729a(17) =156214828a(18) =466736979a(19) =1394894672a(20) =4169810935a(21) =12467680862a(22) =37285474803a(23) =111524444760a(24) =333633526937a(25) =998233861836