Diagonal sums of a triangle based on the Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =20a(5) =59a(6) =185a(7) =600a(8) =2003a(9) =6833a(10) =23727a(11) =83606a(12) =298313a(13) =1076155a(14) =3920823a(15) =14416987a(16) =53482012a(17) =200151737a(18) =755894009a(19) =2882782933a(20) =11115015138a(21) =43400057683a(22) =172016505877a(23) =694208585423