 | ECS #35: Arrangements |
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1. Description
- Arrangements
- partial permutations (Permutations of n thing)
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( {\rm Sequence} \left( Z \right) ,{\rm Set}
\left( Z \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( n+1 \right) f \left( n \right) + \left( -3-n \right) f
\left( n+1 \right) +f \left( 2+n \right) =0,f \left( 0 \right) =1,f
\left( 1 \right) =2 \right\}
other formats
3.3. Closed form
\displaystyle
{{\rm e}^{1}}\Gamma \left( n+1,1 \right)
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac {{{\rm e}^{x}}}{-1+x}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).