Counting tree (Prufer purfer sequence or sequences)

 

answer

First of all we need to know the nature of a number of times for that point in the tree degree at some point in the sequence appears -1 prufer

Emotional understanding of what, in fact, according to prufer sequence Seeking to push themselves what came out

Provided in the subject to a degree of $ D [] $

First of all d--

Then arranges the composition was out

This is a multi-set number of permutations

From the first n d [1] is the number of $ C_ {n} ^ {d [1]} $ then the remaining nd [1] select d [2] $ C_ {nd [1]} ^ {d [ 2]} and so $

$C_{n}^{d[1]}\times C_{n-d[1]}^{d[2]}\times C_{n-d[1]-d[2]}^{d[3]}\times ……\times C_{n-d[1]-……-d[n-1]}^{d[n]}$

get

$\frac{n!}{\sum\limits_{i=1}^{n}d[i]!}$

High-precision transfer would be finished

Or you had not?

Some special sentence:

The first problem will be the case no solution

Then when only one point of the program number 1

Then when there is a number of degrees scheme point 0 to a special treatment