Combinatorics and Graph Theory · Problem 1.8.11

Fundamentals — David Guichard

Mathematics — Combinatorics · stirling-numbers-extensions

Problem

Under the assumptions that

s(n,0) = s(0,n) = 0

for

n \neq 0

, and

s(n,k) = s(n-1,k-1) - (n-1)s(n-1,k)

, extend the table for

s(n,k)

to all integers, and find a connection to

S(n,k)

similar to that in the previous problem.