 | ECS #1067: A simple regular expression |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( {\rm Union} \left( {\rm Sequence} \left( {
\rm Prod} \left( {\rm Union} \left( Z,Z \right) ,Z \right) \right) ,Z
\right) ,{\rm Sequence} \left( Z \right) \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 2\,f \left( n \right) -f \left( n+2 \right) =0,f \left( 0
\right) =1,f \left( 1 \right) =2,f \left( 2 \right) =4 \right\}
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3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+2\,{{\rm \_Z}}^{2} \right) }1/2\,
\left( 1+2\,\alpha \right) {\alpha}^{-1-n}+
\cases{-1&$n=0$\cr 0&otherwise\cr}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {2\,{x}^{2}+2\,x+1}{-1+2\,{x}^{2}}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).