Category Archives: Bell numbers

A Proof of Dobinski’s Formula for Bell Numbers

Dobinski’s formula entails the following infinite series expression for the nth Bell number : In this post we’ll work through a proof of Dobinski’s formula.  We’ll need four formulas: The Maclaurin series for : . The formula for converting normal powers to falling … Continue reading

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Log-Convexity of the Bell Numbers

A sequence is said to be log-convex if, for all , . In this post I give a short, combinatorial-flavored proof that the Bell numbers are log-convex.  The argument is from my answer here on Math.SE. The combinatorial interpretation of the Bell … Continue reading

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