Having seen your letter in my mailbox, I was both glad and sad.
Seeing your letter in my mailbox made me both glad and sad.
"Having seen" desribes a person, so you need a noun to tell us who that person is.
Having seen your letter, I was both glad and sad. = I saw your letter and I was glad and sad.
Having decided on a plan, the team quickly implemented it. = The team decided on a plan and the team implemented it quickly.
Having opened the box of cookies, Joe was unable to keep from eating all of them. = Joe opened the box and Joe ate them all.