 | ECS #72: Balls and Urns |
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1. Description
Ways to place balls into urns: indistinguishable balls and distinguishable urns
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Sequence} \left( U \right) ,U={\rm Sequence} \left( Z,1
\leq {\rm card} \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) =0,f \left( 0
\right) =1,f \left( 1 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
{2}^{-1+n}+\cases{1/2&$n=0$\cr 0&otherwise\cr}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
{\frac {-1+x}{-1+2\,x}}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).