 | ECS #650: 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 Sequence} \left( {\rm Prod} \left(
{\rm Sequence} \left( Z \right) ,{\rm Union} \left( Z,Z \right)
\right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -3\,n-3 \right) f \left( n \right) +f \left( n+1
\right) =0,f \left( 0 \right) =0,f \left( 1 \right) =1,f \left( 2
\right) =4 \right\}
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3.3. Closed form
\displaystyle
\left( 2/9\,{3}^{n}+\cases{-2/9&$n=0$\cr 1/3&$n=1$\cr 0&otherwise\cr}
\right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {x \left( -1+x \right) }{-1+3\,x}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).