Triangle read by rows: G(s, rho) = ((s-1)!/s)*Sum_{i=0..s-1} ((s-i)/i!)*(s*rho)^i.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =3a(6) =6a(7) =18a(8) =24a(9) =16a(10) =24a(11) =96a(12) =180a(13) =200a(14) =125a(15) =120a(16) =600a(17) =1440a(18) =2160a(19) =2160a(20) =1296a(21) =720a(22) =4320a(23) =12600a(24) =23520a(25) =30870a(26) =28812a(27) =16807a(28) =5040a(29) =35280