The flower looks appropriate for that but a way to guarantee your id is to get a key to woody plants for your geographic region. They are difficult to get through at first but get easier as you go along.I will get more pictures of this (and another plant) in a few days. I'm looking around to find abundant food plants for my ready to hatch hickory horned devils, and I read sumac was one. I thought this and another plant nearby were sumac so I figured I could use them.
Does Kentucky coffee tree sound like a match? The is a slightly overrun front yard and this plant itself was a large woody tree approximately 35 feet tall.
I've been able to find a couple sites with photos showing the leaflets appearing alternate or sub-alternate.I'm not disputing your proposal, but I did notice in photographs that the leaves on the tree of heaven do not alternate on the stem, whereas Zephamps's examples do. There is a feature mentioned that seems to be distinctive, glands on the underneath of the leaves at the base. But I think they may appear later in the season. I'm not sure about that, however, so it may be worth an examination. Here is an example I found:
http://www.forestpests.org/images/768x512/2307007.jpg
Easy way to figure if it is tree of heaven is to take a leaf and rub it up in your hands. It will smell EXACTLY like peanut butter if it is tree of heaven. True story. There is not another tree/tall shrub out there that will smell like that.I'm going to go with Ailanthus altissima, or "tree of heaven". The bark, flower, and leaf characteristics all seem to match. Plus it's an invasive which explains the growth patterns you mentioned. It is indeed all over Michigan. My back yard at my last house was full of it. Grows like a weed. :wall:
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Also, it's hard to tell in your pictures, but in at least one of them it does look like there's some sumac. See if you can find any of the erect, bright red clusters of last years fruits to be sure.