Total height of all symmetrically unique Dyck paths of semilength n.

Terms

a(0) =0a(1) =1a(2) =3a(3) =8a(4) =24a(5) =73a(6) =239a(7) =808a(8) =2839a(9) =10173a(10) =37107a(11) =136778a(12) =508622a(13) =1902931a(14) =7156180a(15) =27020991a(16) =102387426a(17) =389129477a(18) =1482851762a(19) =5664065704a(20) =21681357734a(21) =83154466615a(22) =319486977769