# Stirling numbers of the first kind

```perl
sub Stirling1 (Int \n, Int \k) {
    return 1 unless n || k;
    return 0 unless n && k;
    state %seen;
    (%seen{"{n - 1}|{k - 1}"} //= Stirling1(n - 1, k - 1)) +
    (n - 1) * (%seen{"{n - 1}|{k}"} //= Stirling1(n - 1, k))
}

my $upto = 12;

my $mx = (1..^$upto).map( { Stirling1($upto, $_) } ).max.chars;

put 'Unsigned Stirling numbers of the first kind: S1(n, k):';
put 'n\k', (0..$upto)».fmt: "%{$mx}d";

for 0..$upto -> $row {
    $row.fmt('%-3d').print;
    put (0..$row).map( { Stirling1($row, $_) } )».fmt: "%{$mx}d";
}

say "\nMaximum value from the S1(100, *) row:";
say (^100).map( { Stirling1 100, $_ } ).max;
```

#### Output:

```
Unsigned Stirling numbers of the first kind: S1(n, k):
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
```
