 | ECS #626: 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,{\rm Sequence} \left( {\rm Union}
\left( Z,Z,Z \right) \right) \right) \right\}
other formats
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) =0,f \left( 2
\right) =0,f \left( 3 \right) =6 \right\}
other formats
3.3. Closed form
\displaystyle
\left( 1/27\,{3}^{n}+
\cases{-1/27&$n=0$\cr -1/9&$n=1$\cr -1/3&$n=2$\cr 0&otherwise\cr}
\right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac {{x}^{3}}{-1+3\,x}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).