# Stirling numbers of the first kind

```ruby
func S1(n, k) {     # unsigned Stirling numbers of the first kind
    stirling(n, k).abs
}

const r = (0..12)

var triangle = r.map {|n| 0..n -> map {|k| S1(n, k) } }
var widths   = r.map {|n| r.map {|k| (triangle[k][n] \\ 0).len }.max }

say ('n\k ', r.map {|n| "%*s" % (widths[n], n) }.join(' '))

r.each {|n|
    var str = ('%-3s ' % n)
    str += triangle[n].map_kv {|k,v| "%*s" % (widths[k], v) }.join(' ')
    say str
}

with (100) {|n|
    say "\nMaximum value from the S1(#{n}, *) row:"
    say { S1(n, _) }.map(^n).max
}
```

## Output:

```
n\k 0        1         2         3         4        5        6       7      8     9   10 11 12
0   1
1   0        1
2   0        1         1
3   0        2         3         1
4   0        6        11         6         1
5   0       24        50        35        10        1
6   0      120       274       225        85       15        1
7   0      720      1764      1624       735      175       21       1
8   0     5040     13068     13132      6769     1960      322      28      1
9   0    40320    109584    118124     67284    22449     4536     546     36     1
10  0   362880   1026576   1172700    723680   269325    63273    9450    870    45    1
11  0  3628800  10628640  12753576   8409500  3416930   902055  157773  18150  1320   55  1
12  0 39916800 120543840 150917976 105258076 45995730 13339535 2637558 357423 32670 1925 66 1

Maximum value from the S1(100, *) row:
19710908747055261109287881673376044669240511161402863823515728791076863288440277983854056472903481625299174865860036734731122707870406148096000000000000000000
```

Alternatively, the **S1(n,k)** function can be defined as:

```ruby
func S1((0), (0)) { 1 }
func S1(_, (0))   { 0 }
func S1((0), _)   { 0 }
func S1(n, k) is cached { S1(n-1, k-1) + (n-1)*S1(n-1, k) }
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://trizen.gitbook.io/sidef-lang/programming_tasks/s/stirling_numbers_of_the_first_kind.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.