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Another formulation for Stirling numbers of the second kind
I find another formulation for Stirling numbers of the second kind:
Let $n\ge k\ge 1$. Denote by
$$\mathbb N_<^n := \{ \alpha = (\alpha_1,\cdots,\alpha_n): 0\le \alpha_1\le\cdots\le\alpha_n, \...
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