 | ECS #566: 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 Sequence} \left( {\rm Prod} \left( Z,{\rm Sequence}
\left( Z \right) ,{\rm Union} \left( Z,{\rm Sequence} \left( Z
\right) \right) \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( {n}^{3}+6\,{n}^{2}+11\,n+6 \right) f \left( n \right)
+ \left( -3\,n-9 \right) f \left( n+2 \right) +f \left( n+3 \right) =0,
f \left( 0 \right) =1,f \left( 1 \right) =1,f \left( 2 \right) =8
\right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( 1-3\,{\rm \_Z}+{{\rm \_Z}}^{3}
\right) }-1/9\, \left( -1+2\,{\alpha}^{2}-2\,\alpha \right) {\alpha}^{
-n-1}n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac { \left( -1+x \right) ^{2}}{1-3\,x+{x}^{3}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).