 | ECS #431 |
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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 Prod} \left( Z,B
\right) ,S={\rm Union} \left( C,B \right) \right\}
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3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -2+4\,n \right) f \left( n \right) + \left( 5+3\,n
\right) f \left( 1+n \right) + \left( -3-n \right) f \left( n+2
\right) =0,f \left( 0 \right) =1,f \left( 1 \right) =2,f \left( 2
\right) =3 \right\}
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3.3. Closed form
\displaystyle
{\frac {{2}^{2\,n-2} \left( -1+5\,n \right) \Gamma \left( -1/2+n
\right) }{\sqrt {\pi }\Gamma \left( n+2 \right) }}
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3.4. Asymptotics
4. Ordinary generating function
\displaystyle
1/2-1/2\,\sqrt {1-4\,x}-1/2\,{\frac {-1+\sqrt {1-4\,x}}{x}}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).