How could Rome recognize it as Ecumenical then?
In other words, there must be another formula. Constantinople I was followed by the Council of Ephesus (papal legates arrived late), which confirmed the statements of Constantinople I.
Could it be that the Pope or his legate was invited to Constantinople I but never made it? The Latins seem to think that just inviting the Orthodox is sufficient to make a council "ecumenical." Or, simply declare the Orthodox as schismatics and don't bother calling them!
The Council of Ephesus clearly did not recognize Constantinople I. This is readily seen by reading the definition of Faith, which knows only the Council of Nicaea:
Definition of the faith at Nicaea [6th session 22 July 431]The synod of Nicaea produced this creed:
We believe in one God the Father all powerful, maker of all things both seen and unseen. And in one Lord Jesus Christ, the Son of God, the only-begotten begotten from the Father, that is from the substance of the Father, God from God, light from light, true God from true God, begotten not made, consubstantial with the Father, through whom all things came to be, both those in heaven and those in earth; for us humans and for our salvation he came down and became incarnate, became human, suffered and rose up on the third day, went up into the heavens, is coming to judge the living and the dead. And in the holy Spirit.And those who say "there once was when he was not", and "before he was begotten he was not", and that he came to be from things that were not, or from another hypostasis or substance, affirming that the Son of God is subject to change or alteration these the Catholic and Apostolic Church anathematises.
It seems fitting that all should assent to this holy creed. It is pious and sufficiently helpful for the whole world. But since some pretend to confess and accept it, while at the same time distorting the force of its expressions to their own opinion and so evading the truth, being sons of error and children of destruction, it has proved necessary to add testimonies from the holy and orthodox fathers that can fill out the meaning they have given to the words and their courage in proclaiming it. All those who have a clear and blameless faith will understand, interpret and proclaim it in this way.
When these documents had been read out, the holy synod decreed the following.
1. It is not permitted to produce or write or compose any other creed except the one which was defined by the holy fathers who were gathered together in the holy Spirit at Nicaea.
2. Any who dare to compose or bring forth or produce another creed for the benefit of those who wish to turn from Hellenism or Judaism or some other heresy to the knowledge of the truth, if they are bishops or clerics they should be deprived of their respective charges and if they are laymen they are to be anathematised.
3. In the same way if any should be discovered, whether bishops, clergy or laity, thinking or teaching the views expressed in his statement by the priest Charisius about the incarnation of the only-begotten Son of God or the disgusting, perverted views of Nestorius, which underlie them, these should be subject to the condemnation of this holy and ecumenical synod. A bishop clearly is to be stripped of his bishopric and deposed, a cleric to be deposed from the clergy, and a lay person is to be anathematised, as was said before.
How could Rome recognize it as Ecumenical then?
Well, first, because the Council of Chalcedon and subsequent Councils recognized its creed as the authoritative enlargement of the Nicene Creed quote above. Second, for reasons of peace between the Churches of Rome and Constantinople, Rome gave full recognition to this Council and its Canons, including Canon 3: "Because it is new Rome, the bishop of Constantinople is to enjoy the privileges of honour after the bishop of Rome" at what we style the 8th Ecumenical Council, or the Ignatian Synod.
The Roman Catholic position is that Rome determines what is or is not an Ecumenical Council either by acceptance of its acts and definitions by the Pope or His Legates on the spot, or by subsequent recognition. This is why the Latrocinium is not an Ecumenical Synod, while the Council of Chalcedon is - the Legates voided the former with their famous "Non possumus!" and Pope Leo rejected it by branding it the "Latrocinium" and accepted the later upon the acclaim of the Holy Fathers "Peter has spoken through Leo, anathema to those who think otherwise!"