a(n) = Sum_{k=0..floor(n/3)} binomial(n,k)^2 * binomial(n-2*k,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =10a(4) =33a(5) =76a(6) =370a(7) =1569a(8) =5089a(9) =20584a(10) =88776a(11) =336865a(12) =1336434a(13) =5639869a(14) =22824789a(15) =92230285a(16) =384930529a(17) =1595575648a(18) =6570596764a(19) =27418859721a(20) =114736740808a(21) =478594009281