It needs to find an exponential generating function for the next sequence: $(2^n-1)B_n$. Where $B_n$ is the n-th number of Bernoulli. I found that exponential generating function for sequence of $B_n$ is $B(t)=t/(e^t-1)$. But I do not know what to do with $2^nB_n$. Thank you in advance.
2026-03-26 07:55:05.1774511705
Exponential generating function of product
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Hint 1: what happens if you replace $t$ by $2t$ ?
Hint 2: subtract the two generating functions.