This is an original tsumego by me. The solution sequence for this is not particularly outstanding, but as a tsumego this has value in that this position can easily result from a particular 3-3 invasion jōseki.
Black to play.
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I don't know how white gets the 1-1 stone in any joseki...it's unconditional life if that stone was at a better spot.
Anyway, black R18, white Q18, black T18 makes ko to kill.
To be exact, I didn’t mean that this shape is part of a jōseki sequence, but that a particular jōseki can reasonably often develop into this shape.
First we have the usual q16-r17-r16-q17-p17-p18-o17-o18-n17-n18-m17 corner invasion joseki. Later, because of some fight on the right side, black plays s17-s18-s15 to get extra stones on the right side; white forces t17-s16. Later, black plays the t18 throw-in because it’s sente; white hangs in tough with t19. Later still, black plays m18 and white doesn’t answer; then black plays t16 and white plays n19, and we have the problem shape.
Your solution sequence is correct, although technically it’s a two-step kō to kill.
Solution added.