Here is a slight but useful modification. In D5 instead of the instruction above put '=d$1*d4+c4', and copy that into a huge rectangle. The dollar sign, $, will cause the index that follows it to remain constant. Thus when you copy this into other rows and columns, d$1 will be the element of that column in the first row.

When you again put 1 in c4 you get numbers called
"The Stirling numbers
of the second kind"
.

Binomial coefficients count the number of subsets of an
$n$
element set having
$k$
elements in them. The Stirling number for arguments
$n$
and
$k$
here counts the number of partitions of a set of
$n$
elements into
$k$
disjoint blocks.

0.7 Binomial coefficients count the number of subsets of an
$n$ element set having
$k$ elements in them. The Stirling number here counts the number of partitions of a set of
$n$ elements into
$k$ disjoint blocks. Prove these two statements. Solution