 | ECS #557: A simple regular expression in a labelled universe |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( Z,{\rm Union} \left( {\rm Sequence}
\left( Z \right) ,{\rm Sequence} \left( {\rm Prod} \left( Z,Z \right)
\right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{2}-3\,n-2 \right) f \left( n \right) +f \left( n
+2 \right) =0,f \left( 0 \right) =0,f \left( 1 \right) =2,f \left( 2
\right) =2,f \left( 3 \right) =12 \right\}
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3.3. Closed form
\displaystyle
\left( \sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{2} \right) }1
/2\, \left( \alpha+2 \right) {\alpha}^{-n-1}+
\cases{-1&$n=0$\cr 0&otherwise\cr} \right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac { \left( x+2 \right) x}{-1+{x}^{2}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).