Subfactorial user-defined operator symbol

# Factorial user-defined operator symbol: n!

sub postfix:<!>(UInt $parameter --> UInt) is tighter(&infix:<**>){

return [*] 1..$parameter;

};

# Subfactorial user-defined operator symbol: !n

# Defined as `multi` since prefix `!` is also defined as the boolean negation operator

multi sub prefix:<!>(UInt $parameter) is tighter(&infix:<**>){

my @terms = map {(-1)**$^x/$^x!}, 0..$parameter;

my $sum = [+] @terms;

return $parameter!*$sum;

};

sub combinations(UInt $elements,UInt $extraction){

return $elements!/($extraction!*($elements-$extraction)!);

};

sub permutations(UInt $elements,UInt $extraction){

return $extraction!*combinations($elements,$extraction);

};

say "A set of 9 distinct elements all drawn together has...{combinations(9,9)} combinations, {permutations(9,9)} permutations, and {!9} derangements!";

say 'The first twenty one derangements are:';

my $number = 0;

until $number == 21 {

say !$number;

$number++;

};