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

Terms

a(0) =1a(1) =0a(2) =3a(3) =3a(4) =6a(5) =24a(6) =16a(7) =90a(8) =105a(9) =250a(10) =561a(11) =765a(12) =2143a(13) =3108a(14) =6861a(15) =12985a(16) =22221a(17) =47988a(18) =79463a(19) =161451a(20) =293610a(21) =535836a(22) =1042188a(23) =1835898a(24) =3534766a(25) =6399198a(26) =11805756a(27) =22021232a(28) =39718497a(29) =74193924