a(n) = floor((2*n+2)^n/(n+1)!) - binomial(2*n,n).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =13a(5) =93a(6) =569a(7) =3225a(8) =17498a(9) =92473a(10) =480626a(11) =2471344a(12) =12620821a(13) =64183465a(14) =325644870a(15) =1650517964a(16) =8364825118a(17) =42417264804a(18) =215318284778