Who is responsible to pay for the damage done my a neighbor's trampoline blown and smashed a window?

Typically, the responsibility for damage caused by a neighbor's trampoline would fall on the owner of the trampoline, as they are generally liable for any damage their property causes. Homeowners' insurance might cover the costs associated with the damage to your window. It's advisable to discuss the situation with your neighbor and potentially file a claim with their insurance if necessary. If a resolution cannot be reached, legal advice may be needed to determine liability.