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Sometimes the rule S(n,k) = 0 if k>n is given for completeness

VERY important if you dont realize n elements ... k non-empty subsets and you just start with

```
for \$n (0..10) {
for \$k (0..10) {
print "\$n \$k '.fs(\$n,\$k)."\n";
}
}

```use strict; use warnings;

my \$l='k ';
\$l.=sprintf "%3d ",0;
for my \$k (0..10){
\$l.=sprintf " %10s",\$k;
}
print \$l."\n";
\$l=~s/./-/g;
print \$l."\n";

for my \$n (0..10){
printf "n %3d ",\$n;
for my \$k (0..10){
printf " %10s",fs(\$n,\$k);
}
print "\n";
}

sub fs {
my \$n=shift;
my \$k=shift;

if ( \$n ==0 && \$k == 0 ) {return 1};
if ( \$k > \$n ) {return 0};           # important
if ( \$n > 0 && \$k == 0 ) {return 0}
if ( \$k == 1 )            {return 1}
if (\$n == \$k )           {return 1}
my \$p1=fs(\$n-1,\$k-1);
my \$p2=fs(\$n-1,\$k  );
return \$p1 + (\$k*\$p2);
}
And i learned never to name my subroutines s
```use strict; use warnings;

my \$l='k ';
\$l.=sprintf "%3d ",0;
for my \$k (0..10){
\$l.=sprintf " %10s",\$k;
}
print \$l."\n";
\$l=~s/./-/g;
print \$l."\n";

for my \$n (0..10){
printf "n %3d ",\$n;
for my \$k (0..10){
printf " %10s",s(\$n,\$k);
}
print "\n";
}

sub s {
my \$n=shift;
my \$k=shift;

if ( \$n ==0 && \$k == 0 ) {return 1};
if ( \$k > \$n ) {return 0};           # important
if ( \$n > 0 && \$k == 0 ) {return 0}
if ( \$k == 1 )            {return 1}
if (\$n == \$k )           {return 1}
my \$p1=s(\$n-1,\$k-1);
my \$p2=s(\$n-1,\$k  );
return \$p1 + (\$k*\$p2);
}
output
```Global symbol "\$p2" requires explicit package name at buk-2.pl line 30
+.
syntax error at buk-2.pl line 31, near "return"
(Might be a runaway multi-line ;; string starting on line 29)
Global symbol "\$p1" requires explicit package name at buk-2.pl line 31
+.
Global symbol "\$p2" requires explicit package name at buk-2.pl line 31
+.
Missing right curly or square bracket at buk-2.pl line 32, at end of l
+ine
syntax error at buk-2.pl line 32, at EOF
Execution of buk-2.pl aborted due to compilation errors.

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