 | ECS #636: 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 Prod} \left( Z,{\rm Sequence} \left( Z \right) ,{\rm
Sequence} \left( {\rm Prod} \left( Z,Z,Z \right) \right) \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -39\,n-29\,{n}^{2}-{n}^{4}-18-9\,{n}^{3} \right) f
\left( n \right) + \left( -5\,n-6-{n}^{2} \right) f \left( n+1
\right) + \left( -3-n \right) f \left( n+2 \right) + \left( n+2
\right) f \left( n+3 \right) =0,f \left( 0 \right) =0,f \left( 1
\right) =1,f \left( 2 \right) =2 \right\}
other formats
3.3. Closed form
\displaystyle
\left( 1/3\,n+1/3+\sum _{\alpha={\rm RootOf} \left( {{\rm \_Z}}^{2}+{
\rm \_Z}+1 \right) }-1/9\, \left( 2\,\alpha+1 \right) {\alpha}^{-1-n}
\right) n!
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
{\frac {x}{ \left( -1+x \right) \left( -1+{x}^{3} \right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).