 | ECS #567: 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 Union} \left( {\rm Sequence} \left( Z \right) ,{\rm
Sequence} \left( {\rm Prod} \left( Z,Z,Z,Z \right) \right) \right)
\right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{4}-24-10\,{n}^{3}-35\,{n}^{2}-50\,n \right) f
\left( n \right) +f \left( n+4 \right) =0,f \left( 0 \right) =2,f
\left( 1 \right) =1,f \left( 2 \right) =2,f \left( 3 \right) =6,f
\left( 4 \right) =48 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{{\rm \_Z}}^{4} \right) }1/4\,
\left( {\alpha}^{3}+{\alpha}^{2}+2\,\alpha+1 \right) {\alpha}^{-1-n}n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac {{x}^{3}+{x}^{2}+x+2}{-1+{x}^{4}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).