Looping Factorial that adds successive terms

Writing a code that add sucessive terms but the denominator increases in increments of 1!.

So in example

p(x) = yi +ma(1) + a(2) m(m-1)/2!

I am unable to write a for loop that adds sucessive terms. Here is what I have

for m_2=2:n
    mprod = mprod*((m+(1-(m_2-1)))/factorial(m_2-1));
    yi = yi +a(m_2)*mprod;
end

My code i believe doesnt increase the factorials rather multiples them

[Rik]

It is not clear to me what your inputs are and how the calculations should be expanded. Can you give a few examples?

[David Ramirez]

I hope this helps this clears up what I was saying. The denominator just multiplies factorials rather than replacing it. I figured the rest out but I cannot get the denominator correct.

Answer 1

[Rik]

You should have just shown the last line. I first spent quite some time finding the correct method of implementing your non-desired output, instead of jumping immediately on the desired ouput.

%generate/pick some values
m=4;%this code also works for m=1, in which case it will return yi unchanged
a=rand(m+1,1);
yi=0;

%factors for the elements of a:
%m            /    1
%m*(m-1)      /    1*2
%m*(m-1)*(m-2)/    1*2*3

numerator=m-( 0:(m-2) );
numerator=cumprod(numerator);

divisor=1:(m-1);
divisor=cumprod(divisor);

mprod=numerator./divisor;
mprod=reshape(mprod,[],1);%make the products the same shape as a(2:m)

%perform actual calculation
yi=yi + sum( a(2:m).*mprod );

The values in mprod seem extremely predictable. You should probably have a look at how to produce it directly, instead of dividing large numbers. At some point you will generate too large values and inaccuracies will creep in that you could avoid. I will leave that as an excersize for you.