Sequential coalitions

one trillion is 10 ¹²

I am sorry but I am not familiar with your terminology.

list all the sequential coalitions of 25 players?
Do you mean all the possible combinations of 25 players, whether there is/are 1,2,3,.....or 25 players in the individual group?

ok, I've done some research and i think that you mean all the possible groups of 1 player plus all the possible groups of 2 players up to all the possible groups of 25 players. But the order the players are chosen is also important.
I used excel to help me get the answer.
I got 4.21638E+25 different permutations possible
I divided this by a trillion to get the number of seconds it would take
then I divided by 60 to get minutes
then I divided by 60 to get hours
then I divided by 24 to get days
then I divided by 365.25 to get years

My answer is 1,336,091 years.

permutations 131021.JPG