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*******************************
*** Math::Combinatorics *******
...
      +-----------------------------------------------------------+
     500     1000    1500    2000    2500   3000    3500    4000

use strict;
use warnings;
...
    return $sum
}

f(4,0)*2**3  f(3,0)*2**2  f(2,0)*2**1  f(1,0)*2**0  f(0,0)*2**0
f(4,1)*2**2  f(3,1)*2**1  f(2,1)*2**0  f(1,1)*2**0
f(4,2)*2**1  f(3,2)*2**0  f(2,2)*2**0
f(4,3)*2**0  f(3,3)*2**0
f(4,4)*2**0

sub func { $_[0] ** 2 * $_[1] }
sub group_hero_blunt {
...
    }
    return $sum
}

sub group_hero_better {
    use bigint;
...
    }
    return $sum
}