 | ECS #143 |
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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( Z,1\leq {\rm card} \right) ,C={\rm
Union} \left( {\rm Epsilon},Z \right) ,E={\rm Prod} \left( B,C \right)
,S={\rm Sequence} \left( E,1\leq {\rm card} \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n \right) +2\,f \left( n+1 \right) -f \left( n+2
\right) =0,f \left( 0 \right) =0,f \left( 1 \right) =1,f \left( 2
\right) =3 \right\}
other formats
3.3. Closed form
\displaystyle
\sum _{\alpha={\rm RootOf} \left( -1+2\,{\rm \_Z}+{{\rm \_Z}}^{2}
\right) }1/2\,{\alpha}^{-n}+\cases{-1&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {x \left( 1+x \right) }{-1+2\,x+{x}^{2}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).