 | ECS #849: 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
Union} \left( Z,B \right) ,S={\rm Cycle} \left( C \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{3}-3\,{n}^{2}-2\,n \right) f \left( n \right) +
\left( 12\,n+8+4\,{n}^{2} \right) f \left( n+1 \right) + \left( -8-4\,
n \right) f \left( n+2 \right) +f \left( n+3 \right) =0,f \left( 0
\right) =0,f \left( 1 \right) =2,f \left( 2 \right) =6,f \left( 3
\right) =34,f \left( 4 \right) =276 \right\}
other formats
3.3. Closed form
\displaystyle
-\Gamma \left( n \right) -3/2\, \left( 3/2-1/2\,\sqrt {5} \right) ^{n-
2}\Gamma \left( n \right) \sqrt {5}+7/2\, \left( 3/2-1/2\,\sqrt {5}
\right) ^{n-2}\Gamma \left( n \right) +7/2\, \left( 1/2\,\sqrt {5}+3/
2 \right) ^{n-2}\Gamma \left( n \right) +3/2\, \left( 1/2\,\sqrt {5}+3
/2 \right) ^{n-2}\Gamma \left( n \right) \sqrt {5}
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
\ln \left( -{\frac {-1+x}{1-3\,x+{x}^{2}}} \right)
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).