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Leucocholia (talk | contribs) Changed rising factorial notation to avoid ambiguity with repeated differentiation |
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with {{math|1=''f''<sub>0</sub> = 0}} and {{math|''f''<sub>1</sub> ≠ 0}}, then an explicit form of inverse coefficients can be given in term of [[Bell polynomial]]s:<ref>Eqn (11.43), p. 437, C.A. Charalambides, ''Enumerative Combinatorics,'' Chapman & Hall / CRC, 2002</ref>
:<math> g_n = \frac{1}{f_1^n} \sum_{k=1}^{n-1} (-1)^k n^\overline{
where
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\hat{f}_k &= \frac{f_{k+1}}{(k+1)f_{1}}, \\
g_1 &= \frac{1}{f_{1}}, \text{ and} \\
n^{
\end{align}</math>
is the [[rising factorial]].
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