 | ECS #30: Cycles Set |
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1. Description
Permutation with at least two cycles
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Set} \left( {\rm Cycle} \left( Z \right) ,2\leq {\rm
card} \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{2}-2\,n-1 \right) f \left( n+1 \right) +f
\left( n+2 \right) n=0,f \left( 0 \right) =0,f \left( 1 \right) =0,f
\left( 2 \right) =1,f \left( 3 \right) =4 \right\}
other formats
3.3. Closed form
\displaystyle
\Gamma \left( n \right) \left( n-1 \right)
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
- \left( x-\ln \left( - \left( -1+x \right) ^{-1} \right) +\ln
\left( - \left( -1+x \right) ^{-1} \right) x \right) \left( -1+x
\right) ^{-1}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).