a(n) = binomial(2*n-2,n-1) - n.

Terms

a(0) =0a(1) =0a(2) =3a(3) =16a(4) =65a(5) =246a(6) =917a(7) =3424a(8) =12861a(9) =48610a(10) =184745a(11) =705420a(12) =2704143a(13) =10400586a(14) =40116585a(15) =155117504a(16) =601080373a(17) =2333606202a(18) =9075135281a(19) =35345263780a(20) =137846528799a(21) =538257874418