Sum of trapezoid weights of all Motzkin paths of length n.

Terms

a(0) =0a(1) =1a(2) =3a(3) =10a(4) =28a(5) =80a(6) =224a(7) =633a(8) =1793a(9) =5109a(10) =14619a(11) =42003a(12) =121089a(13) =350116a(14) =1014892a(15) =2948429a(16) =8582357a(17) =25024833a(18) =73080783a(19) =213714517a(20) =625756147a(21) =1834282280a(22) =5382370208a(23) =15808450470a(24) =46470788358a(25) =136715063545a(26) =402505866459