 | ECS #284: Trees |
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1. Description
Planar trees with arity 1
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Prod} \left( Z,S \right) ,S={\rm Sequence} \left( B
\right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 2+4\,n \right) f \left( n \right) + \left( -2-n
\right) f \left( n+1 \right) =0,f \left( 0 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
{\frac {{4}^{n}\Gamma \left( n+1/2 \right) }{\sqrt {\pi }\Gamma
\left( 2+n \right) }}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-1/2\,{\frac {-1+\sqrt {1-4\,x}}{x}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).