(01/28/2011, 10:42 PM)Gottfried Wrote:(01/28/2011, 09:12 PM)mike3 Wrote: Well, here goes... this is LONG! I'm going to also give an explanation of the derivation, since you were asking for more "insight" into the problem.
Very interesting! and not soo long at all. I cannot chew it instantly but I'll take my time tomorrow and on sunday to interprete and relate it to the matrix-notation. Now since I see that 2,3,3,4,3,4,4,5,... pattern and the string-concatenation I get the impression that this might be one of the cases where the recursive description is replaced by an expansion back to the initial parameter(s), but where no obvious simplification is found - which would reflect my experience that I couldn't find a shorter description for the schröder-coefficients than by the explicite matrix-eigendecomposition (for the triangular case). But well - this is just an impression by the first reading, perhaps it is completely false.
Anyway - thanks so far. I'll try to understand everything next two days.
Gottfried
Upps: one question: the r's in this posts are the chi's of the earlier one?
Woo, that post was not actually finished, I had hit "post" too soon! There's more information there now.
And \( r_{n, m} \) would equal, in this case, \( r_{n, m} = \frac{u^{n-1}}{1 - u^{n-1}} \frac{m!}{n!} \left{{n \atop m}\right} \).
