A problem in two parts:

1. Code a (possibly recursive) solution to generalise the following "calculation".

   my $total = calcIt( $N, $depth );

2. Define a formula for calculating the total without going through the motions.

   The innermost sum can be replaced by $_ * ( $_ + 1 ) / 2.

   Can the rest of the process be replaced by a formula in terms of $N & $depth?

I believe the values produced are related to Binomial coefficients C(n, d). of various dimensions--but that's where I get stuck.

use List::Util qw[ sum ];

$N = 10; 
print sum map{ 
    sum map{ 
        sum map{ 
            sum map{ 
                sum map{ 
                    sum 0 .. $_ 
                } 0 .. $_ 
            } 0 .. $_ 
       } 0 .. $_ 
    } 0 .. $_ 
} 0 .. $N;;
11440

$N = 20; 
print sum map{ 
    sum map{ 
        sum map{ 
            sum map{ 
                sum map{ 
                    sum 0 .. $_ 
                } 0 .. $_ 
            } 0 .. $_ 
        } 0 .. $_ 
    } 0 .. $_ 
} 0 .. $N;;
657800
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