 | ECS #570: 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 Union} \left( {\rm Prod} \left( {\rm Sequence} \left( Z
\right) ,{\rm Sequence} \left( Z \right) \right) ,{\rm Prod} \left( Z
,Z \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -n-2 \right) f \left( n \right) +f \left( n+1 \right)
=0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2 \right) =8,f
\left( 3 \right) =24,f \left( 4 \right) =120,f \left( 5 \right) =720
\right\}
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3.3. Closed form
\displaystyle
\left( n+1+\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}^{2}-2\,{x}^{3}+{x}^{4}}{ \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).