Number of nondecreasing Motzkin paths of length n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =9a(5) =21a(6) =49a(7) =115a(8) =269a(9) =630a(10) =1474a(11) =3450a(12) =8073a(13) =18893a(14) =44212a(15) =103465a(16) =242125a(17) =566617a(18) =1325982a(19) =3103035a(20) =7261648a(21) =16993545a(22) =39767898a(23) =93063924a(24) =217786044a(25) =509657890a(26) =1192689641a(27) =2791104828a(28) =6531679192a(29) =15285285161