 | ECS #77 |
| Introduction | Examples | Search | Submit | Help | Links |
1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ B={\rm Set} \left( Z,1\leq {\rm card} \right) ,S={\rm Prod}
\left( B,B \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ f \left( n+2 \right) +2\,f \left( n \right) -3\,f \left( n+1
\right) =0,f \left( 0 \right) =0,f \left( 1 \right) =0,f \left( 2
\right) =2 \right\}
other formats
3.3. Closed form
\displaystyle
-2+{2}^{n}
other formats
3.4. Asymptotics
4. Exponential generating function
\displaystyle
\left( {{\rm e}^{x}} \right) ^{2}-2\,{{\rm e}^{x}}+1
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) -2=0,y \left( 0 \right) =0,
\mbox {D} \left( y \right) \left( 0 \right) =0 \right\}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).