a(n) = n*Sum_{i=0..n-1} binomial(n,i)*binomial(i-1,n-i-1)/(n-i).

Terms

a(0) =0a(1) =1a(2) =3a(3) =10a(4) =27a(5) =76a(6) =210a(7) =589a(8) =1659a(9) =4708a(10) =13428a(11) =38479a(12) =110682a(13) =319411a(14) =924339a(15) =2681410a(16) =7794939a(17) =22702396a(18) =66229212a(19) =193495279a(20) =566069052a(21) =1658026093a(22) =4861703289a(23) =14269842184a(24) =41922504570a(25) =123265254451a(26) =362719839225