Addendum I thank David Fowler for pointing out that John Wallis exhibited “Stirling numbers of the first kind” in several formulas for figurate numbers, for example on page 162 of his Arithmetica …

7/6, etc. These coefficients seem to grow at an alarming rate, but eventually they settle down somewhat; Stirling's approximation tells us that am+1000 = (m + 1000)m/m! ~ (1+ …

Stirling subset number \becomes Stirling partition number \endchange \amendpage 4a.829 new entry in the rightmost column (23.05.05) Algorithm 7.2.1.5P, 428. \endchange \amendpage …

P152 On the inversion of y-to-the-alpha times e-to-the-y by means of associated Stirling numbers.

The basic recurrence for Stirling partition numbers, m +1 d +1 =( d +1) + , (3 . 4) is based on the fact that a partition of m girls into d +1 nonempty blocks either puts the oldest girl into a ( d + 1) …

(See section 3 of my unpublication ``Poly-Bernoulli Bijections.'') @d maxn 25 /* Stirling partition numbers will be less than $2^{61}$ */ @c #include <stdio.h> #include <stdlib.h> int m,n; /* …

they settle down somewhat; Stirling's approximation tells us that $a_{m+1000} =(m+1000)^m\!/m!\approx(1+1000/m)^me^m\!/\sqrt{2\pi m} \approx e^{1000+m}\!/\sqrt{2\pi …