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

Terms

a(0) =0a(1) =1a(2) =4a(3) =18a(4) =100a(5) =675a(6) =5376a(7) =49294a(8) =510728a(9) =5894109a(10) =74915740a(11) =1039180186a(12) =15613569324a(13) =252501251743