a(n) = Sum_{k=0..floor((n+1)/2)} (k+1) * A008315(n, k).

Terms

a(0) =1a(1) =3a(2) =5a(3) =13a(4) =24a(5) =58a(6) =111a(7) =257a(8) =500a(9) =1126a(10) =2210a(11) =4882a(12) =9632a(13) =20980a(14) =41531a(15) =89497a(16) =177564a(17) =379438a(18) =754014a(19) =1600406a(20) =3184016a(21) =6720748a(22) =13382710a(23) =28117498a(24) =56026984a(25) =117254268a(26) =233765636a(27) =487589572a(28) =972504704a(29) =2022568168