 | ECS #838: A simple grammar |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( Z,1\leq {\rm card} \right) ,C={\rm
Prod} \left( B,B \right) ,S={\rm Cycle} \left( C \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 2\,{n}^{2}+2\,n \right) f \left( n \right) + \left( -3
\,n-3 \right) f \left( n+1 \right) +f \left( n+2 \right) =0,f \left( 0
\right) =0,f \left( 1 \right) =0,f \left( 2 \right) =2,f \left( 3
\right) =12 \right\}
other formats
3.3. Closed form
\displaystyle
2\, \left( -1+{2}^{-1+n} \right) \Gamma \left( n \right)
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
\ln \left( -{\frac { \left( -1+x \right) ^{2}}{-1+2\,x}} \right)
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).