Some tutors are very irresponsible, they copied a solution from other website, sadly it's not even for this question. Please be more responsible! Thank you!

Branching with immigration. Each generation of a branching process (with a single progenitor} is augmented by a random number of immigrants who are indistinguishable from the other members of the population. Suppose that the numbers of immigrants in different generations are independent of each other and of the past historyr of the branching process, each such number having probability generating function H (3}. Show that the probability generating function G\" of the size of the nth generation satises 034.1(3) : GR(G(3)}H{3], where G is the probability generating function of a typical familyr of offspring