 | ECS #559: 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( {\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( -11\,{n}^{3}-41\,{n}^{2}-30-61\,n-{n}^{4} \right) f
\left( n \right) + \left( -{n}^{2}-5\,n-6 \right) f \left( n+1
\right) + \left( -n-3 \right) f \left( n+2 \right) +f \left( n+4
\right) -f \left( n+3 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =1,f \left( 2 \right) =2,f \left( 3 \right) =6 \right\}
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3.3. Closed form
\displaystyle
\left( 5/8+\sum _{\alpha={\rm RootOf} \left( {{\rm \_Z}}^{3}+{{\rm \_Z
}}^{2}+{\rm \_Z}+1 \right) }1/16\, \left( {\alpha}^{2}+2\,\alpha-1
\right) {\alpha}^{-1-n}+1/4\,n \right) n!
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3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {1}{ \left( -1+x \right) \left( -1+{x}^{4} \right) }}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).