Sum array of Catalan numbers (A000108) read by upward antidiagonals.

Terms

a(0) =1a(1) =2a(2) =1a(3) =5a(4) =3a(5) =2a(6) =15a(7) =10a(8) =7a(9) =5a(10) =51a(11) =36a(12) =26a(13) =19a(14) =14a(15) =188a(16) =137a(17) =101a(18) =75a(19) =56a(20) =42a(21) =731a(22) =543a(23) =406a(24) =305a(25) =230a(26) =174a(27) =132a(28) =2950a(29) =2219