Generalized ballot numbers (first differences of Motzkin numbers).

Terms

a(0) =0a(1) =1a(2) =2a(3) =5a(4) =12a(5) =30a(6) =76a(7) =196a(8) =512a(9) =1353a(10) =3610a(11) =9713a(12) =26324a(13) =71799a(14) =196938a(15) =542895a(16) =1503312a(17) =4179603a(18) =11662902a(19) =32652735a(20) =91695540a(21) =258215664a(22) =728997192a(23) =2062967382a(24) =5850674704a(25) =16626415975a(26) =47337954326a(27) =135015505407a(28) =385719506620