In　this　paper　we　derive　and　compare　numerical　sequences　obtained　by　adapted　polynomials　such　as　HOMFLYPT,　Jones　and　Alexander-Conway　for　the　topological　cascade　of　vortex　torus　knots　and　links　that　progressively　untie　by　a　single　reconnection　event　at　a　time.　Two　cases　are　considered:　the　alternate　sequence　of　knots　and　co-oriented　links　(with　positive　crossings)　and　the　sequence　of　two-component　links　with　oppositely　oriented　components　(negative　crossings).　New　recurrence　equations　are　derived　and　sequences　of　numerical　values　are　computed.　In　all　cases　the　adapted　HOMFLYPT　polynomial　proves　to　be　the　best　quantifier　for　the　topological　cascade　of　torus　knots　and　links.