a(n) = Sum_{k=0..2n} (k+1) * A027023(n,2n-k).

Terms

a(0) =1a(1) =6a(2) =19a(3) =56a(4) =165a(5) =486a(6) =1435a(7) =4248a(8) =12601a(9) =37438a(10) =111367a(11) =331608a(12) =988181a(13) =2946662a(14) =8791447a(15) =26241632a(16) =78359825a(17) =234069830a(18) =699404127a(19) =2090385216a(20) =6249236653a(21) =18686125070a(22) =55884824535a(23) =167164064984a(24) =500102988889