 | ECS #544: 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 Union} \left( Z,Z,{\rm Prod}
\left( Z,Z,Z \right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{3}-6\,{n}^{2}-11\,n-6 \right) f \left( n
\right) + \left( -2\,n-6 \right) f \left( n+2 \right) +f \left( n+3
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2
\right) =8 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+2\,{\rm \_Z}+{{\rm \_Z}}^{3}
\right) }{\frac {1}{59}}\, \left( 16+12\,{\alpha}^{2}+9\,\alpha
\right) {\alpha}^{-n-1}n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
- \left( -1+2\,x+{x}^{3} \right) ^{-1}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).