Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k valleys.

Terms

a(0) =2a(1) =5a(2) =1a(3) =14a(4) =7a(5) =1a(6) =42a(7) =36a(8) =11a(9) =1a(10) =132a(11) =165a(12) =80a(13) =16a(14) =1a(15) =429a(16) =715a(17) =484a(18) =155a(19) =22a(20) =1a(21) =1430a(22) =3003a(23) =2639a(24) =1183a(25) =273a(26) =29a(27) =1a(28) =4862a(29) =12376