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Aug 2, 2022 at 15:21 vote accept Iosif Pinelis
Apr 29, 2022 at 19:42 comment added Iosif Pinelis @IraGessel : Thank you for your comment.
Apr 29, 2022 at 19:40 comment added Ira Gessel The coefficients of $2g(t)$, as an exponential generating function, are sequence A211393 of the OEIS (oeis.org/A211393) and this formula for $\ln(2g(t))$ can be found there.
Apr 29, 2022 at 19:38 comment added Iosif Pinelis @ChristopheLeuridan : Thank you for your comment. That $2t$ was multiplied by $\frac12$, which you may not have noticed. I have now rewritten the expression in an equivalent, but slightly simpler, form.
Apr 29, 2022 at 19:36 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 29, 2022 at 19:32 comment added Christophe Leuridan @losif Pinelis By computing the sum of the two fractions defining $f(t)$, I find the same answer, excepted that I have $t \tanh^{-1}(t)$ instead of $2t \tanh^{-1}(t)$. But I get the same final formula.
Apr 29, 2022 at 19:27 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 29, 2022 at 19:16 history answered Iosif Pinelis CC BY-SA 4.0