Lah numbers: Difference between revisions

=={{header|Ruby}}==

Works with Ruby 3.0 (end-less method; end-less and begin-less range).

<lang ruby>def fact(n) = n.zero? ? 1 : 1.upto(n).inject(&:*)

def lah(n, k)

return 0 if n < 1

case k

when 1 then fact(n)

when n then 1

when (..1),(n..) then 0

else (fact(n)*fact(n-1)) / (fact(k)*fact(k-1)) / fact(n-k)

end

end

r = (0..12)

puts "Unsigned Lah numbers: L(n, k):"

puts "n/k #{r.map{|n| "%11d" % n}.join}"

r.each do |row|

print "%-4s" % row

puts "#{(0..row).map{|col| "%11d" % lah(row,col)}.join}"

end

puts "\nMaximum value from the L(100, *) row:";

puts (1..100).map{|a| lah(100,a)}.max

</lang>

{{out}}

<pre>Unsigned Lah numbers: L(n, k):

n/k 0 1 2 3 4 5 6 7 8 9 10 11 12

0 0

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

siep@siep-desktop:~$

</pre>