 | ECS #600: 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 Sequence} \left( {\rm Prod} \left( Z,{\rm Sequence}
\left( {\rm Prod} \left( Z,{\rm Union} \left( Z,Z \right) \right)
\right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -2\,{n}^{2}-6\,n-4 \right) f \left( n \right) +
\left( -2-n \right) f \left( n+1 \right) +f \left( n+2 \right) =0,f
\left( 0 \right) =1,f \left( 1 \right) =1,f \left( 2 \right) =2
\right\}
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3.3. Closed form
\displaystyle
\left( \sum _{\alpha={\rm RootOf} \left( -1+2\,{{\rm \_Z}}^{2}+{\rm
\_Z} \right) }-1/9\, \left( -2+\alpha \right) {\alpha}^{-1-n}+
\cases{1&$n=0$\cr 0&otherwise\cr} \right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {-1+2\,{x}^{2}}{-1+2\,{x}^{2}+x}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).