Ha! I was just looking at the same thing:
https://ejje.weblio.jp/sentence/content/たまるものか
I think you may be right. It might be a shortening of たまるものか.
So maybe something like:
How could I have forgotten something / on the 15th floor?
(Genuine question.)
Nice!
Yeah I discarded that right away but I like to look at as many options as possible. lol
Nice work! I actually tried to see if there were any set phrases but came up empty so your Google-fu must be strong. 
I’ll have to do some more thinking to see how this impacts my translation, which I wasn’t sure about anyway. 
From the first link @Myria sent (I, of course, read them in reverse order — never fails):
～て堪る is followed most frequently by either か or ものか to show that one would never let something happen.
[Edit: Can’t believe I’d never been to imabi.net before — wow, there’s some great content there!]
So now I’m wondering if it might mean something like:
I’ll never forget something if lost-and-found is on the 15th floor
Ooh yeah, I’m leaning toward that being the one. 
Confirmation from #1 daughter that that’s the closest so far.
She says 〜してたまるか is basically like 絶対に〜したくない/しないぞ. The correct kanji would be 堪る (but most people would use hiragana) and the phrase is short for 堪るものか.
She struggles to translate this one without adding words, too, but says it’s something like “I vow to never forget anything from (my/the room) on the 15th floor.” There’s an implication they live or work there.
Looking like @Myria wins definitively today!
This thread is the most fun I’ve had learning in a long while. 
- 忘れ物してたまるかの十五階
わすれもの・してたまるかの・じゅうごかい
I vow never to forget anything from (my room/the office?) on the 15th floor
Notes:
@Myria for helping us to figure this one out!Volume: Salaryman
354.「鬼は外」 鬼が豆まき オレは外
Hints:
Remember to please use the spoiler tag with your translation attempts! Also, please include the reading in kana with your submission.
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Here’s the link to the spreadsheet with all the upcoming senryu as well as the translations to date.
354.「鬼は外」 鬼が豆まき オレは外
おにはそと おにがまめまき おれはそと
“Demons outside!” The demon’s scattering beans, I am outside.
Hmm. I know about Setsubun. Chuckin’ beans at a person in an oni mask and yelling “Oni out! Fortune in!” to drive away evil spirits and purify the home, but I’m not sure what’s happening in this poem. I don’t think I’ve interpreted it quite right.
Is it an “I am the bad luck in this house” type thing? I could also picture like, someone’s kid in the oni mask flingin’ beans at his dad and not quite understanding the assignment.
You aren’t alone!
The author says the demons/ogres/devils are throwing the beans and he or she is the one outside, but what that means isn’t exactly spelled out.
I’m inclined to think the “demons” are just the kids in masks throwing beans at the their dad going to (or coming home from) work. It’s not uncommon for the kids to want to wear the masks and throw the beans! (Speaking from experience.)
Haha okay good, that was kind of the mental image I was getting.
354.「鬼は外」 鬼が豆まき オレは外
おにはそと おにがまめまき おれはそと
“Oni outside!” / The Oni is bean scattering / It’s me outside
My interpretation here is that the dad is dressing up, like he does every year, and he’s doing so with a bit of a resigned smile. My only real clue for that is that it’s in the Salaryman category.
The problem with Dad being the oni is that 鬼が豆まき, the oni are the ones throwing/sowing the beans.
I’m unsure: is it 撒く (to scatter) or 蒔く (to sow)? Never occurred to me that there was even a difference, much less to ask this question.
Edit: Kenkyusha says it’s the former:
日本では節分の夜, 家の内外に豆をまく. In Japan on the eve of the first day of spring, people scatter dry beans around the inside and outside of their home.
Edit 2: Ooh! This is interesting. Apparently, it also has the connotation of “giving someone the slip”:
(I’ve head the まいた version a lot. It never occurred to me that this was a conjugation of まく!)
I think that still jives since the gag is that he’s the Oni, or dressed up as it at least.
Ah that’s interesting. I don’t know if it would apply here though since 豆まき is a specific thing, but it could be a play on that.
Yeah, I don’t think it applies here, but I’m learning there’s more to these things than are apparent at first glance! <laugh> (Also: you’ve got a typo. I think you meant “that still jibes”.)
I thought you threw the beans to chase the oni out of the house, though. I don’t get how dad would be the one throwing if he’s got the mask on?
Ah good point. Hmm.
Maybe the dad is throwing beans at himself in the Oni mask since the rest of the family can’t be bothered?
Or maybe he’s a true サラリマン and has no family so he’s doing the whole ritual solo?
Nah I meant jives. Although the word did come from jibe originally. It just sounds more gangsta 
Not checked anyone else’s or read the discussion so maybe it’ll be totally off, but I want to try.
“Out with the devil!” [The devil is scattering beans.] “Out with me, I guess.”
A little clumsy, but it’s all I could think for my interpretation. Basically I read this as taking place on 節分, and the speaker is doing 豆撒き to banish the oni (and more metaphorically, bad fortune) from the house, but then the devil basically plays a reverse Uno card and banishes the speaker instead. I’m not that confident with this one; on top of language ambiguities I am autistic so if there’s some symbolic representation of a social interaction I am apt to miss it. But I wanted to try, so I made myself do it. Please be nice.
Now to read the discussion and feel embarrassed about having posted this 
In regard to the 鬼が豆まき, could it be saying that the oni/Dad is taking part in the general activity of the豆まき, regardless of which role he plays? Sort of like '鬼(のオレ)が豆まき(活動するので、外にいる). Total guess, just something I thought of.
Don’t worry about it. I haven’t posted the last couple of days, but I get them wrong a lot, and I couldn’t make heads or tails of this one. I’m still not sure I agree with any of the attempts either, I can’t quite figure this one out, even with all of the translations people have posted.
Ok, I am having a lot of trouble with understanding this one, because I think I don’t really have any context about setsubun. But, my thought is, maybe…
It’s setsubun, the kids are saying there are oni outside, and they are throwing beans. But the dad thinks the kids are oni, and he goes outside to avoid the beans?
So for instance, “There’s oni outside! But actually, the oni are the ones throwing the beans. Now I’m outside.”
Nice job, and welcome to the club!