 | ECS #562: 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 Union} \left( Z,{\rm Sequence}
\left( Z \right) \right) ,{\rm Sequence} \left( {\rm Union} \left( Z,
Z \right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 2\,{n}^{2}+6\,n+4 \right) f \left( n \right) + \left(
-3\,n-6 \right) f \left( n+1 \right) +f \left( n+2 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =4,f \left( 2 \right) =18,f \left( 3
\right) =114 \right\}
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3.3. Closed form
\displaystyle
\left( -1+5\,{2}^{-1+n}+\cases{-1/2&$n=0$\cr 0&otherwise\cr} \right) n
!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac {-x+{x}^{2}-1}{ \left( -1+x \right) \left( -1+2\,x \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).