The number $12$ (or, probably we shall say Bernoulli numbers in general) appears in many places in Mathematics, sometimes leading to unexpected connections between different topics.

For instance, some time ago there was a very interesting explanation for

1) its occurrence in the Todd class

and

2) its occurrence in the Euler-Maclaurin formula

in terms of Riemann-Roch for toric varieties, as explained in:

Euler-Maclaurin formula and Riemann-Roch

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My question is, will there be some relation between 1) and

3) its occurrence in the Baker-Campbell-Hausdorff formula.

I guess this might be related to some explicit local expressions in some method of proving the index theorem on Lie groups, or even the Duflo map (which I don't really understand).

Thank you very much.