 | ECS #499: 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,Z,Z,{\rm Sequence}
\left( 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( -n-3 \right) f \left( n+2 \right) +f \left( n+3
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =0,f \left( 2
\right) =0 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{\rm \_Z}+{{\rm \_Z}}^{3} \right)
}-1/31\, \left( 2+3\,{\alpha}^{2}-11\,\alpha \right) {\alpha}^{-1-n}n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {-1+x}{-1+x+{x}^{3}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).