polynomials with increasing order

For the specific form outlined with all unity coefficients (and actually for any as Steven shows), Matlab already has the function--it's polyval. Ignoring the numerics issue on the hope you'll restrict [N,x] to reasonable values it's simply

N=4;
x=0.3;
y=polyval(ones(N,1),x);

It's simple enough to rewrite this just a little via a function handle so only the order and x is required

>> poly=@(n,x) polyval(ones(n,1),x);
>> n=3;
>> x=[0:0.1:0.4];
>> poly(n,x)
ans =
  1.0000    1.1100    1.2400    1.3900    1.5600
>>

NB: it's already vectorized as well.

You can deal with the issue of coefficients for the terms and even the order of the terms(*) if desired similarly.

(*) If you're adamant you want the order to be from constant to increasing power-of-x, then

poly=@(n,x) polyval(fliplr(ones(n,1)),x);

IOW, your function poly simply swaps the order in which it passes the coefficients to polyval--it's transparent to the use later. Of course, you have to be consistent and remember you can't pass the coefficient vector directly to the Matlab function.

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