If you plot it:
Eqn = @(n) (n-1)./factorial(n-1).*exp(-(n-1)).*(n-1).^(n-1)-0.38;
n = 1:5;
y = Eqn(n);
figure(1)
plot(n, Eqn(n))
grid
you can see that the equation is satisfied as closely as it can be at n = 2.
I set it up the way I did initially to use it with the fzero function, so it will produce a zero-crossing. Replacing factorial(n-1) with gamma(n) and letting fzero solve it produces n = 2.058.
