 | ECS #17: Set partitions |
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1. Description
- Set partitions with all blocks of size <=2
- self-conjugate permutations on n letters
- involution numbers a(n)=a(n-1)+(n-1)a(n-2)
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Set} \left( {\rm Union} \left( {\rm Set} \left( Z,{\rm
card}=1 \right) ,{\rm Set} \left( Z,{\rm card}=2 \right) \right)
\right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -n-1 \right) f \left( n \right) +f \left( n+2 \right)
-f \left( n+1 \right) =0,f \left( 0 \right) =1,f \left( 1 \right) =1
\right\}
other formats
3.3. Asymptotics
4. Exponential generating function
\displaystyle
{{\rm e}^{x+1/2\,{x}^{2}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).