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Topic: Difficult expression, possible to simplify to (n+1)^(n-1)?
Replies: 1   Last Post: Feb 28, 1998 3:22 AM

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Dan Aaronson

Posts: 10
Registered: 12/7/04
Difficult expression, possible to simplify to (n+1)^(n-1)?
Posted: Feb 26, 1998 4:37 AM
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During work om my math thesis i have come across a strange expression
that it seems to
be possible to simplify quite a lot.
When you count the number of complete exceptional sequences over the
hereditary algebra An you get the expression I for convenience have
attached in a Sci.Word file.
The original hypothesis was however that I would get (n+1)^(n-1), and
when you test the
two expressions in maple you find that the difference is 0 at least up
to n=11.
I would like to get a proof that the two expressions are equal for all
positive integers,
and, no, you can not use the binomial rule because the terms x and y in
(x+y)^n change
for each term inside the expression.

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\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}


$\Sigma _{i=1}^{n}\binom{n}{i}(n-i+1)^{n-i-1}(i+1)^{i}$



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