Generalized or s-Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =1a(7) =5a(8) =12a(9) =22a(10) =1a(11) =14a(12) =55a(13) =140a(14) =285a(15) =1a(16) =42a(17) =273a(18) =969a(19) =2530a(20) =5481a(21) =1a(22) =132a(23) =1428a(24) =7084a(25) =23751a(26) =62832a(27) =141778a(28) =1a(29) =429