 | ECS #635: 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( {\rm Sequence} \left( Z \right) ,{\rm
Union} \left( Z,{\rm Sequence} \left( {\rm Prod} \left( 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}-8\,{n}^{2}-17\,n-10 \right) f \left( n
\right) + \left( -n-2 \right) f \left( n+1 \right) + \left( n+4
\right) f \left( n+2 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =2,f \left( 2 \right) =6,f \left( 3 \right) =18,f \left( 4
\right) =96 \right\}
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3.3. Closed form
\displaystyle
\left( 7/4+1/2\,n+1/4\, \left( -1 \right) ^{-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+{x}^{3}-1}{ \left( -1+x \right) \left( -1+{x}^{2} \right)
}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).