 | ECS #836: A simple grammar |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ B={\rm Set} \left( Z,1\leq {\rm card} \right) ,C={\rm Sequence
} \left( Z,1\leq {\rm card} \right) ,S={\rm Prod} \left( B,C \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 3\,n+{n}^{2}+2 \right) f \left( n \right) + \left( -4-
{n}^{2}-4\,n \right) f \left( 1+n \right) + \left( 1+n \right) f
\left( n+2 \right) =0,f \left( 0 \right) =0,f \left( 1 \right) =0,f
\left( 2 \right) =2 \right\}
other formats
3.3. Closed form
\displaystyle
{\frac {\Gamma \left( 1+n \right) \left( -\Gamma \left( n \right) +{
{\rm e}^{1}}\Gamma \left( n,1 \right) \right) }{\Gamma \left( n
\right) }}
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
-{\frac {x \left( {{\rm e}^{x}}-1 \right) }{-1+x}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).