A generalized Chebyshev transform of the Motzkin numbers A001006.

Terms

a(0) =1a(1) =1a(2) =4a(3) =8a(4) =25a(5) =65a(6) =197a(7) =571a(8) =1753a(9) =5351a(10) =16746a(11) =52626a(12) =167547a(13) =536559a(14) =1732272a(15) =5622960a(16) =18357211a(17) =60205319a(18) =198323708a(19) =655787680a(20) =2176141555a(21) =7244106347a(22) =24185285341a(23) =80960692691a(24) =271685400443a(25) =913784117809