Središčni binomski koeficient: Razlika med redakcijama

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Središčni binomski koeficient (uredi)

Redakcija: 00:37, 12. maj 2016

dodanih 78 zlogov ,  pred 6 leti
m
m+/dp/slog
m (m/dp/tn)
m (m+/dp/slog)
|width="25px"|  ||width="25px"|  ||width="25px"|  ||width="25px"| 
|width="25px"|  ||width="25px"| 
|width="25px" align="center"|<math>\mathbf underline{1}</math> ||width="25px"|&nbsp;
|width="25px"|&nbsp; ||width="25px"|&nbsp; ||width="25px"|&nbsp; ||width="25px"|&nbsp;
|width="25px"|&nbsp; ||width="25px"|&nbsp; ||width="25px"|&nbsp; ||width="25px"|&nbsp;
|-
|&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp;
|align="center"|<math>1</math> ||&nbsp; ||align="center"|<math>\mathbf underline{2}</math> ||&nbsp; ||align="center"|<math>1</math>
|&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp;
|-
|&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp;
|align="center"|<math>1</math> ||&nbsp; ||align="center"|<math>4</math> ||&nbsp;
|align="center"|<math>\mathbf underline{6}</math> ||&nbsp; ||align="center"|<math>4</math> ||&nbsp;
|align="center"|<math>1</math> ||&nbsp;
|&nbsp; ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp;
|&nbsp; ||&nbsp; ||&nbsp; ||&nbsp;
|align="center"|<math>1</math> ||&nbsp; ||align="center"|<math>6</math> ||&nbsp;
|align="center"|<math>15</math> ||&nbsp; ||align="center"|<math>\mathbfunderline{20}</math> ||&nbsp;
|align="center"|<math>15</math> ||&nbsp; ||align="center"|<math>6</math> ||&nbsp;
|align="center"|<math>1</math> ||&nbsp; ||&nbsp; ||&nbsp; ||&nbsp;
|&nbsp; ||&nbsp; ||align="center"|<math>1</math> ||&nbsp; ||align="center"|<math>8</math> ||&nbsp;
|align="center"|<math>28</math> ||&nbsp; ||align="center"|<math>56</math> ||&nbsp;
|align="center"|<math>\mathbf underline{70}</math> ||&nbsp; ||align="center"|<math>56</math> ||&nbsp;
|align="center"|<math>28</math> ||&nbsp; ||align="center"|<math>8</math> ||&nbsp;
|align="center"|<math>1</math> ||&nbsp; ||&nbsp;
|align="center"|<math>1</math> ||&nbsp; ||align="center"|<math>10</math> ||&nbsp; ||align="center"|<math>45</math> ||&nbsp;
|align="center"|<math>120</math> ||&nbsp; ||align="center"|<math>210</math> ||&nbsp;
|align="center"|<math>\mathbf underline{252}</math> ||&nbsp; ||align="center"|<math>210</math> ||&nbsp;
|align="center"|<math>120</math> ||&nbsp; ||align="center"|<math>45</math> ||&nbsp;
|align="center"|<math>10</math> ||&nbsp; ||align="center"|<math>1</math>
 
: <math> A_{10,10} = \begin{bmatrix}
\mathbfunderline{1}& 1& 1& 1& 1& 1& 1& 1& 1& 1\\
1& \mathbfunderline{2}& 3& 4& 5& 6& 7& 8& 9& 10\\
1& 3& \mathbfunderline{6}& 10& 15& 21& 28& 36& 45& 55\\
1& 4& 10& \mathbfunderline{20}& 35& 56& 84& 120& 165& 220\\
1& 5& 15& 35& \mathbfunderline{70}& 126& 210& 330& 495& 715\\
1& 6& 21& 56& 126& \mathbfunderline{252}& 462& 792& 1287& 2002\\
1& 7& 28& 84& 210& 462& \mathbfunderline{924}& 1716& 3003& 5005\\
1& 8& 36& 120& 330& 792& 1716& \mathbfunderline{3432}& 6435& 11440\\
1& 9& 45& 165& 495& 1287& 3003& 6435& \mathbfunderline{12870}& 24310\\
1& 10& 55& 220& 715& 2002& 5005& 11440& 24310& \mathbfunderline{48620}
\end{bmatrix} \; , </math>
 
Sorodna [[Catalanovo število|Catalanova števila]] ''C''<sub>''n''</sub> so dana z:
 
: <math> C_{n} = \frac{1}{n+1} {2n \choose n} = {2n \choose n} - {2n \choose n+1} = \frac{(2n)!}{n! \; (n+1)!}, \qquad (n \geq 0) \!\, . </math>
 
Preprosta posplošitev središčnih binomskih koeficientov je dana kot:
Vzpostavljeno iz »https://sl.wikipedia.org/wiki/Posebno:MobileDiff/4643891«

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