 | ECS #258: Binomial coefficients |
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1. Description
Arrangements of n unlabelled objects in 9 rows
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( Z \right) ,S={\rm Prod} \left( B,B,B,B
,B,B,B,B,B \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -40320\,f \left( n \right) +{n}^{8}+36\,{n}^{7}+546\,{n}^{6}+
4536\,{n}^{5}+22449\,{n}^{4}+67284\,{n}^{3}+118124\,{n}^{2}+109584\,n+
40320=0,f \left( 0 \right) =1 \right\}
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3.3. Closed form
\displaystyle
{\frac {1}{40320}}\, \left( n+1 \right) \left( n+2 \right) \left( n+3
\right) \left( n+4 \right) \left( n+5 \right) \left( n+6 \right)
\left( n+7 \right) \left( n+8 \right)
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
- \left( -1+x \right) ^{-9}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).