Inverse Euler Transform of the Motzkin Numbers.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =10a(5) =22a(6) =56a(7) =136a(8) =348a(9) =890a(10) =2332a(11) =6136a(12) =16380a(13) =43988a(14) =119170a(15) =324720a(16) =890290a(17) =2452752a(18) =6789308a(19) =18868520a(20) =52635730a(21) =147323176a(22) =413618614a(23) =1164510896a(24) =3287073450a(25) =9300500508a(26) =26372968632a(27) =74937133488a(28) =213333642442a(29) =608400799010