View source for Lah numbers

=={{header|Swift}}==

{{libheader|AttaSwift BigInt}}
{{trans|Kotlin}}

<syntaxhighlight lang="swift">import BigInt
import Foundation

@inlinable
public func factorial<T: BinaryInteger>(_ n: T) -> T {
  guard n != 0 else {
    return 1
  }

  return stride(from: n, to: 0, by: -1).reduce(1, *)
}

@inlinable
public func lah<T: BinaryInteger>(n: T, k: T) -> T {
  if k == 1 {
    return factorial(n)
  } else if k == n {
    return 1
  } else if k > n {
    return 0
  } else if k < 1 || n < 1 {
    return 0
  } else {
    let a = (factorial(n) * factorial(n - 1))
    let b = (factorial(k) * factorial(k - 1))
    let c = factorial(n - k)

    return a / b / c
  }
}

print("Unsigned Lah numbers: L(n, k):")
print("n\\k", terminator: "")

for i in 0...12 {
  print(String(format: "%10d", i), terminator: " ")
}

print()

for row in 0...12 {
  print(String(format: "%-2d", row), terminator: "")

  for i in 0...row {
    lah(n: BigInt(row), k: BigInt(i)).description.withCString {str in
      print(String(format: "%11s", str), terminator: "")
    }
  }

  print()
}

let maxLah = (0...100).map({ lah(n: BigInt(100), k: BigInt($0)) }).max()!

print("Maximum value from the L(100, *) row: \(maxLah)")</syntaxhighlight>

{{out}}


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