 | ECS #112 |
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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 Prod} \left( B,B \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 4\,f \left( n \right) -4\,f \left( n+1 \right) +f \left( n+2
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2
\right) =5 \right\}
other formats
3.3. Closed form
\displaystyle
1/4\,{2}^{n}n+1/4\,{2}^{n}+{2}^{-1+n}+
\cases{1/4&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac { \left( -1+x \right) ^{2}}{ \left( -1+2\,x \right) ^{2}}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).