a(n) = Sum_{k=0..n} (k+1) * A026769(n, n-k).

Terms

a(0) =1a(1) =3a(2) =8a(3) =23a(4) =59a(5) =158a(6) =395a(7) =1023a(8) =2522a(9) =6414a(10) =15694a(11) =39486a(12) =96226a(13) =240470a(14) =584762a(15) =1454777a(16) =3533743a(17) =8763720a(18) =21276031a(19) =52642872a(20) =127770797a(21) =315574532a(22) =765852193a(23) =1888788990a(24) =4583560631a(25) =11290381790a(26) =27397549743a(27) =67414670138