a(n) = Sum_{k=0..[n/2]} C(n-k,k)^2 * n/(n-k), n>=1.

Terms

a(0) =1a(1) =3a(2) =7a(3) =15a(4) =36a(5) =87a(6) =211a(7) =519a(8) =1285a(9) =3198a(10) =7998a(11) =20079a(12) =50571a(13) =127725a(14) =323367a(15) =820407a(16) =2085306a(17) =5309169a(18) =13537045a(19) =34561890a(20) =88347091a(21) =226079208a(22) =579110262a(23) =1484766015a(24) =3809948461a(25) =9783998877a(26) =25143452881a(27) =64658016249a(28) =166375274790