A mean binomial transform of the Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =3a(3) =8a(4) =27a(5) =97a(6) =373a(7) =1493a(8) =6163a(9) =26027a(10) =111897a(11) =488006a(12) =2153429a(13) =9596199a(14) =43121211a(15) =195165576a(16) =888861555a(17) =4070582971a(18) =18732710281a(19) =86584519280a(20) =401776434017