local int = require "int"
local fmt = require "fmt"

$alias fact = int.factorial

local function lah(n, k)
    if k == 1 then return fact(n) end
    if k == n then return 1 end
    if k > n  then return 0 end
    if k < 1 or n < 1 then return 0 end
    return (fact(n) * fact(n - 1)) // (fact(k) * fact(k - 1)) // fact(n - k)
end

print("Unsigned Lah numbers: l(n, k):")
io.write("n/k")
for i = 0, 12 do fmt.write("%10d ", i) end
print("\n" .. string.rep("-", 145))
for n = 0, 12 do
    fmt.write("%2d ", n)
    for k = 0, n do fmt.write("%10d ", lah(n, k)) end
    print()
end