I wanted to know if it is possible to use exponential generating functions to evaluate composition of N using K distinct numbers (where the supply of numbers is infinite)?
For e.g if N=10 and a1=2,a2=3,a3=5
then number of solutions would be (2,3,5),(2,5,3),(3,2,5),(3,5,2),(5,2,3),(5,3,2),(2,2,2,2,2),(3,3,2,2),(3,2,2,3),(2,2,3,3),(2,3,2,3),(3,2,3,2),(2,3,3,2)
I tried with writing generating functions for 2,3 and 5 but was not able to deduce anything.