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Notamathematician
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Algorithm for the sum with binomial coefficients and Bell numbers
$\exp(-x)$ instead of $\exp(x)$, isn't it?
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Generating function for A261041
Thank you for answer! Could you add a proof of the equivalence of the two expressions for $B(x)$?
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Generating function for A261041
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Algorithm for the sum with binomial coefficients and Bell numbers
@PietroMajer, when we compute $\nu_{j+1}$ we use the new one just computed $\nu_j$. In the algorithm, everything works according to the standard assignment rules. Just read the question again or experiment with the PARI/GP program.
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Generating function for A225114
@DimaPasechnik, you can start with OEIS A005169.
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Generating function for A225114
@DimaPasechnik, done.
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Generating function for A225114
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