a(n) = Sum_{k=0..n} (k+1) * A026758(n, n-k).

Terms

a(0) =1a(1) =3a(2) =8a(3) =23a(4) =55a(5) =149a(6) =339a(7) =889a(8) =1966a(9) =5059a(10) =10985a(11) =27939a(12) =59898a(13) =151210a(14) =321155a(15) =806806a(16) =1701347a(17) =4260511a(18) =8933737a(19) =22325426a(20) =46600476a(21) =116300505a(22) =241846731a(23) =603086027a(24) =1250175771a(25) =3116094702a(26) =6442311137a(27) =16054097455a(28) =33114584924