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

Terms

a(0) =1a(1) =0a(2) =2a(3) =2a(4) =3a(5) =12a(6) =7a(7) =36a(8) =41a(9) =84a(10) =186a(11) =230a(12) =612a(13) =852a(14) =1733a(15) =3198a(16) =5112a(17) =10628a(18) =16873a(19) =32562a(20) =57463a(21) =99892a(22) =188103a(23) =319188a(24) =591982a(25) =1040076a(26) =1849352a(27) =3351304a(28) =5854119a(29) =10610416