Sum of the heights of all Motzkin paths of length n.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =9a(5) =25a(6) =70a(7) =196a(8) =552a(9) =1560a(10) =4423a(11) =12573a(12) =35826a(13) =102310a(14) =292786a(15) =839554a(16) =2411945a(17) =6941593a(18) =20011328a(19) =57779038a(20) =167069317a(21) =483739961a(22) =1402413161a(23) =4070537585a(24) =11827842021a(25) =34403798725a(26) =100167396088a(27) =291903951462a(28) =851380987390