a(n) = hypergeom([1, -n, -n-1], [2], 1).

Terms

a(0) =1a(1) =2a(2) =6a(3) =25a(4) =135a(5) =896a(6) =7042a(7) =63841a(8) =654901a(9) =7491574a(10) =94470926a(11) =1301130777a(12) =19423173211a(13) =312256205652