Area under Motzkin paths.

Terms

a(0) =1a(1) =10a(2) =54a(3) =242a(4) =979a(5) =3728a(6) =13627a(7) =48382a(8) =168069a(9) =574040a(10) =1934346a(11) =6446824a(12) =21290563a(13) =69771854a(14) =227150074a(15) =735316478a(16) =2368536349a(17) =7596077384a(18) =24267094264a(19) =77258501372a(20) =245204480443a(21) =776060212130