 | ECS #581: A simple regular expression in a labelled universe |
| Introduction | Examples | Search | Submit | Help | Links |
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,Z,{\rm Sequence}
\left( {\rm Union} \left( Z,Z,Z \right) \right) \right) \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -{n}^{2}-3\,n-2 \right) f \left( n \right) + \left( -3
\,n-6 \right) f \left( n+1 \right) +f \left( n+2 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =0 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+3\,{\rm \_Z}+{{\rm \_Z}}^{2}
\right) }1/13\, \left( -3+11\,\alpha \right) {\alpha}^{-n-1}n!
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {-1+3\,x}{-1+3\,x+{x}^{2}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).