@Axel Vogt The procedure produced by rsolve with option makeproc uses a "sliding window" such that it saves the previous three computed values. Aside from error checking, it's equivalent to this:

X:= proc(n)
     local k,L,r;
     L:= [0,1,2]; #Initial values
     for k from 3 to n do
          r:= `+`((k*L)[]);
          L:= [L[2], L[3], r]
     end do;
     L[4+n-k]
end proc:

@mois Can you show the exact command that you used and the results that it returned? Also, why didn't you do the model function f:= a+b*x^c+d*x^e?

Yes, please "send" the document (worksheet) by attaching it to a Reply.

By the way, your English is fine by MaplePrimes standards. Try to make a better title though.

As a moderator, I changed this Question's title from "A Rounding bug in maple" to "Is this a Rounding bug in maple?"

@Sujaan Kunalan There is no way to explicitly mark a Question as answered, but you can "vote up" for the Answer by clicking on the "thumb up" icon in the upper right corner of the Answer.

@Mac Dude The only thing that makes the difference in your call to NonlinearFit is the initialvalues. All Statistics package routines that take a Vector will take a list also.

@Markiyan Hirnyk Quoting from ?combine:

For many functions, the transformations applied by combine are the inverse of the transformations that are applied by expand. For example, consider the well-known identity
           sin(a + b) = sin(a) cos(b) + cos(a) sin(b)
The combine function applies the identity from right to left, whereas the expand function does the reverse.

You wrote: What is the reasoning behind the output?

The reasoning is that the result should also be valid for n=0.

@Alex Smith Why [-90,1] and not [-90,0]? Also, you can hide the z-axis label.

plot3d(
     [x,y,0], x= 0..1, y= 0..1-x,
     axes= boxed, labels= [x,y,``], style= patchnogrid, orientation= [-90,0]
);

x:= [2,3,5,1,4]:
y:= [1,2,3,4,5]:
H:= table(x =~ y):
convert(H, list);
 

The default built-in ordering that sort uses for listlists is lexicographic, so the following works and is more efficient than sorting with a user-supplied total-ordering procedure:

sort([[2,1],[3,2],[5,3],[1,4],[4,5]]);

                  [[1, 4], [2, 1], [3, 2], [4, 5], [5, 3]]

@Joe Riel Oh, I just misunderstood your last sentence to mean that the attributes trick could be done simpler, faster, and smaller in a loop. You just meant a straightforward max-finding loop. It's all clear now.

Please repost the array Data in a plaintext form so that I can cut-and-paste it.

@Joe Riel I'm having trouble understanding your last sentence---why it's simpler, faster, smaller. Could you show an example doing it in a do loop?

It just requires a slight modification of the original:

add(s^LL[1]*t^LL[2]/mul(x!, x= LL), LL= L);