 | ECS #138 |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( {\rm Set} \left( Z,1\leq {\rm card}
\right) ,{\rm Set} \left( Z \right) \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n+2 \right) -3\,f \left( n+1 \right) +2\,f \left( n
\right) =0,f \left( 0 \right) =0,f \left( 1 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
-1+{2}^{n}
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
\left( {{\rm e}^{x}} \right) ^{2}-{{\rm e}^{x}}
other formats
It satisfies the following differential equation of order 2:
\displaystyle
\left\{ {\frac {d^{2}}{d{x}^{2}}}y \left( x \right) -3\,{\frac {d}{dx}
}y \left( x \right) +2\,y \left( x \right) =0,y \left( 0 \right) =0,
\mbox {D} \left( y \right) \left( 0 \right) =1 \right\}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).