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An earlier version is A036040, a special case of the Faa di Bruno formula. These partition polynomials are known also as the complete Bell polynomials and are a refinement of the Stirling polynomials of the second kind. - Tom Copeland, Jun 11 2021
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Cf. A036040, another version.
An earlier version is A036040, a special case of the Faa di Bruno formula. These partition polynomials are known also as the complete Bell polynomials and are a refinement of the Stirling polynomials of the second kind. - Tom Copeland, Jun 11 2021
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editing
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nmax = 20; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k]*x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 08 2021 *)
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