 | ECS #578: 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 Union} \left( Z,{\rm Prod}
\left( Z,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}^{5}-15\,{n}^{4}-85\,{n}^{3}-225\,{n}^{2}-274\,n-
120 \right) f \left( n \right) + \left( -n-5 \right) f \left( n+4
\right) +f \left( n+5 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =1,f \left( 2 \right) =2,f \left( 3 \right) =6,f \left( 4
\right) =24 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+{\rm \_Z}+{{\rm \_Z}}^{5} \right)
}{\frac {1}{3381}}\, \left( 256+320\,{\alpha}^{4}+400\,{\alpha}^{3}+500
\,{\alpha}^{2}+625\,\alpha \right) {\alpha}^{-1-n}n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
- \left( -1+x+{x}^{5} \right) ^{-1}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).