a(n) = C(n,2)*Bell(n-2) (cf. A000217, A000110).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =12a(5) =50a(6) =225a(7) =1092a(8) =5684a(9) =31572a(10) =186300a(11) =1163085a(12) =7654350a(13) =52928460a(14) =383437327a(15) =2902665885a(16) =22907918640a(17) =188082362120