 | ECS #50: Unary-binary trees |
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1. Description
- Unlabelled unary-binary trees
- Motzkin numbers (Generalized ballot numbers)
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( Z,{\rm Sequence} \left( S,{\rm card}\leq 2
\right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 3\,nf \left( n \right) + \left( 3+2\,n \right) f \left( 1+n
\right) + \left( -3-n \right) f \left( n+2 \right) =0,f \left( 0
\right) =0,f \left( 1 \right) =1 \right\}
other formats
3.3. Asymptotics
4. Ordinary generating function
\displaystyle
-1/2\,{\frac {-1+x+\sqrt {1-2\,x-3\,{x}^{2}}}{x}}
other formats
5. References
- Motzkin
- EIS A001006
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).