Difficult sequence puzzle

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What is the 25$^{th}$ term of this infinite sequence?

$$1,1,1,1,1,691,2,3617,...$$

I have tried for an hour now and I can't find any meaningful relation between the terms.

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This is the sequence of numerators of taylor series expansion of $\log(x/\sin(x))$ as can be seen in the online encyclopedia of integer sequences: OEIS.org

The next term is $43867$.