a(n) = Sum_{k=0..2n} (k+1) * A027113(n, 2n-k).

Terms

a(0) =1a(1) =7a(2) =26a(3) =85a(4) =264a(5) =803a(6) =2422a(7) =7281a(8) =21860a(9) =65599a(10) =196818a(11) =590477a(12) =1771456a(13) =5314395a(14) =15943214a(15) =47829673a(16) =143489052a(17) =430467191a(18) =1291401610a(19) =3874204869a(20) =11622614648a(21) =34867843987a(22) =104603532006a(23) =313810596065a(24) =941431788244