 | ECS #602: 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( Z,{\rm Prod} \left( {
\rm Sequence} \left( Z \right) ,{\rm Sequence} \left( Z \right)
\right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{2}-2\,n-1 \right) f \left( n \right) +f \left( n
+1 \right) n=0,f \left( 0 \right) =0,f \left( 1 \right) =1,f \left( 2
\right) =6,f \left( 3 \right) =18,f \left( 4 \right) =96,f \left( 5
\right) =600 \right\}
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3.3. Closed form
\displaystyle
\left( n+\cases{1&$n=0$\cr 0&otherwise\cr} \right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {x \left( x-2\,{x}^{2}+{x}^{3}+1 \right) }{ \left( -1+x \right)
^{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).