 | ECS #609: 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 Union} \left( Z,{\rm Prod}
\left( Z,{\rm Sequence} \left( {\rm Prod} \left( Z,Z \right) \right)
\right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 11\,n+6+{n}^{3}+6\,{n}^{2} \right) f \left( n \right)
+ \left( -{n}^{2}-5\,n-6 \right) f \left( n+1 \right) + \left( -6-2\,n
\right) f \left( n+2 \right) +f \left( n+3 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =2,f \left( 2 \right) =8 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-{{\rm \_Z}}^{2}-2\,{\rm \_Z}+{{\rm
\_Z}}^{3} \right) }1/7\, \left( 2+\alpha \right) {\alpha}^{-n-1}n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac {-1+{x}^{2}}{1-{x}^{2}-2\,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).