Number of down-steps (1,-1) among all n-length nondecreasing Dyck paths with air pockets.

Terms

a(0) =1a(1) =0a(2) =2a(3) =3a(4) =7a(5) =15a(6) =33a(7) =72a(8) =157a(9) =341a(10) =738a(11) =1591a(12) =3417a(13) =7312a(14) =15593a(15) =33145a(16) =70242a(17) =148443a(18) =312893a(19) =657944a(20) =1380437a(21) =2890349a(22) =6040258a(23) =12600623a(24) =26243057a(25) =54572320a(26) =113321233a(27) =235002417a(28) =486735682a(29) =1006950771