 | ECS #552: 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,{\rm Sequence}
\left( {\rm Prod} \left( Z,Z,Z \right) \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}^{2}-5\,n-6 \right) f \left( n+1 \right) +f
\left( n+3 \right) =0,f \left( 0 \right) =1,f \left( 1 \right) =0,f
\left( 2 \right) =2,f \left( 3 \right) =0 \right\}
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3.3. Closed form
\displaystyle
\left( \sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{3}+{{\rm \_Z}
}^{2} \right) }-1/23\, \left( 6\,{\alpha}^{2}+2\,\alpha-9 \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+{x}^{3}}{-1+{x}^{3}+{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).