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Lah numbers: Difference between revisions
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=={{header|zkl}}==
<lang zkl>fcn lah(n,k,fact=fcn(n){ [1..n].reduce('*,1) }){
if(n==0 or k==0) return(0);
if(n==k) return(1);
if(k==1) return(fact(n));
(fact(n)*fact(n - 1)) /(fact(k)*fact(k - 1)) /fact(n - k)
}</lang>
<lang zkl>// calculate entire table (quick), find max, find num digits in max
N,mx := 12, [1..N].apply(fcn(n){ [1..n].apply(lah.fp(n)) }).flatten() : (0).max(_);
fmt:="%%%dd".fmt("%d".fmt(mx.numDigits + 1)).fmt; // "%9d".fmt
println("Unsigned Lah numbers: L(n,k):");
println("n\\k",[0..N].pump(String,fmt));
foreach row in ([0..N]){
println("%3d".fmt(row), [0..row].pump(String, lah.fp(row), fmt));
}</lang>
{{out}}
<pre style="font-size:83%">
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
</pre>
{{libheader|GMP}} GNU Multiple Precision Arithmetic Library
<lang zkl>var [const] BI=Import("zklBigNum"); // libGMP
N=100;
println("Maximum value from the L(%d, *) row:".fmt(N));
[1..N].apply(lah.fpM("101",BI(N),fcn(n){ BI(n).factorial() }))
.reduce(fcn(m,n){ m.max(n) }).println();</lang>
{{out}}
<pre style="font-size:83%">
Maximum value from the L(100, *) row:
44519005448993144810881324947684737529186447692709328597242209638906324913313742508392928375354932241404408343800007105650554669129521241784320000000000000000000000
</pre>
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