a(n) = Sum_{k=0..n} C(n+k,k)*C(n+k,n-k).

Terms

a(0) =1a(1) =3a(2) =16a(3) =95a(4) =591a(5) =3780a(6) =24620a(7) =162423a(8) =1081780a(9) =7258053a(10) =48982176a(11) =332140328a(12) =2261099491a(13) =15444137880a(14) =105789736896a(15) =726426836103