 | ECS #114 |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( C \right) ,C={\rm Sequence} \left( Z,0
<{\rm card} \right) ,S={\rm Union} \left( C,B \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -2\,f \left( n \right) +f \left( n+1 \right) +1=0,f \left( 0
\right) =1,f \left( 1 \right) =2,f \left( 2 \right) =3 \right\}
other formats
3.3. Closed form
\displaystyle
1+{2}^{-1+n}+\cases{-1/2&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {x+{x}^{2}-1}{ \left( -1+x \right) \left( -1+2\,x \right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).