Sum[k=1..n, T(k,n-k+1)], where T is array A094718.

Terms

a(0) =1a(1) =2a(2) =4a(3) =6a(4) =11a(5) =16a(6) =29a(7) =43a(8) =78a(9) =119a(10) =217a(11) =340a(12) =624a(13) =1000a(14) =1847a(15) =3015a(16) =5602a(17) =9282a(18) =17341a(19) =29084a(20) =54605a(21) =92512a(22) =174455a(23) =298110a(24) =564332a(25) =971562a(26) =1845363a(27) =3198129a(28) =6092037a(29) =10621152