a(n) = Sum_{k=0..n} (k+1) * binomial(k,2*(n-k)).

Terms

a(0) =1a(1) =2a(2) =3a(3) =7a(4) =17a(5) =36a(6) =72a(7) =143a(8) =282a(9) =549a(10) =1057a(11) =2019a(12) =3832a(13) =7232a(14) =13581a(15) =25394a(16) =47303a(17) =87819a(18) =162549a(19) =300060a(20) =552552a(21) =1015259a(22) =1861674a(23) =3407433a(24) =6226053a(25) =11358407a(26) =20691504a(27) =37642816a(28) =68395609a(29) =124127202