DERANGEMENT

gistfile1.matlab

%% CLOSED-FORM DERANGEMENT
function d = derangements(n)
  numerator = (ones(1,n+1)*-1).^(0:n);
  denomerator = arrayfun(@factorial, 0:n);
  factorial_terms = numerator ./ denomerator;
  d = sum(factorial(n) * factorial_terms)

%% RECURSIVE DERANGEMENT
function der = deraangements_rec(n)
  der = NaN(1,n);
  for m=0:n
    d = factorial(m);
    for k=1:m
      d = d- nchoosek(m,k)*der(m-k+1);
    end
    der(m+1) = d;
  end
  der = sum(der);