# Lah numbers

``````func lah(n, k) {
stirling3(n, k)
#binomial(n-1, k-1) * n!/k!     # alternative formula
}

const r = (0..12)

var triangle = r.map {|n| 0..n -> map {|k| lah(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 L(#{n}, *) row:"
say { lah(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         2          1
3   0         6          6          1
4   0        24         36         12          1
5   0       120        240        120         20          1
6   0       720       1800       1200        300         30         1
7   0      5040      15120      12600       4200        630        42        1
8   0     40320     141120     141120      58800      11760      1176       56       1
9   0    362880    1451520    1693440     846720     211680     28224     2016      72      1
10  0   3628800   16329600   21772800   12700800    3810240    635040    60480    3240     90    1
11  0  39916800  199584000  299376000  199584000   69854400  13970880  1663200  118800   4950  110   1
12  0 479001600 2634508800 4390848000 3293136000 1317254400 307359360 43908480 3920400 217800 7260 132 1

Maximum value from the L(100, *) row:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
``````