 | ECS #265: Arrangements |
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1. Description
Arrangements of n labelled objects in 6 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 \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 120\,f \left( n \right) -{n}^{5}-15\,{n}^{4}-85\,{n}^{3}-225\,
{n}^{2}-274\,n-120=0,f \left( 0 \right) =1 \right\}
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3.3. Closed form
\displaystyle
{\frac {1}{120}}\, \left( n+1 \right) \left( n+2 \right) \left( n+3
\right) \left( n+4 \right) \left( n+5 \right)
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
\left( -1+x \right) ^{-6}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).