 | ECS #395 |
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1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Prod} \left( S,S \right) ,C={\rm Prod} \left( S,B
\right) ,S={\rm Union} \left( B,C,Z \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -3+27\,{n}^{2} \right) f \left( n \right) + \left( 33
\,n+11+22\,{n}^{2} \right) f \left( n+1 \right) + \left( -5\,{n}^{2}-15
\,n-10 \right) f \left( n+2 \right) =0,f \left( 0 \right) =0,f \left( 1
\right) =1,f \left( 2 \right) =1 \right\}
other formats
3.3. Asymptotics
4. Ordinary generating function
\displaystyle
{\rm RootOf} \left( -{\rm \_Z}+{{\rm \_Z}}^{2}+{{\rm \_Z}}^{3}+x
\right)
other formats
It satisfies the following differential equation of order 2:
\displaystyle
\left\{ -1-3\,y \left( x \right) + \left( 27\,x+11 \right) {\frac {d}{
dx}}y \left( x \right) + \left( -5+22\,x+27\,{x}^{2} \right) {\frac {d^
{2}}{d{x}^{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).