 | ECS #411 |
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1. Description
leaves in binary trees or pairs of binary trees
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Prod} \left( C,C \right) ,C={\rm Union} \left( B,Z
\right) ,S={\rm Union} \left( B,C,Z \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( -n-1
\right) f \left( n+1 \right) =0,f \left( 0 \right) =0,f \left( 1
\right) =2 \right\}
other formats
3.3. Closed form
\displaystyle
{\frac {{2}^{-1+2\,n}\Gamma \left( n-1/2 \right) }{\sqrt {\pi }\Gamma
\left( n+1 \right) }}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
1-\sqrt {1-4\,x}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).