 | ECS #610: 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,Z,Z,Z,{\rm Union} \left( Z,{\rm Sequence
} \left( Z \right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -n-1 \right) f \left( n \right) +f \left( n+1 \right)
=0,f \left( 0 \right) =0,f \left( 1 \right) =0,f \left( 2 \right) =0,f
\left( 3 \right) =0,f \left( 4 \right) =24,f \left( 5 \right) =240,f
\left( 6 \right) =720,f \left( 7 \right) =5040 \right\}
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3.3. Closed form
\displaystyle
\left( 1+
\cases{-1&$n=0$\cr -1&$n=1$\cr -1&$n=2$\cr 1&$n=5$\cr -1&$n=3$\cr 0&otherwise\cr}
\right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {{x}^{4} \left( -x+{x}^{2}-1 \right) }{-1+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).