 | ECS #396 |
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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,C \right) ,C={\rm Prod} \left( S,S,Z
\right) ,S={\rm Union} \left( Z,C,B \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 279\,n+279\,{n}^{2} \right) f \left( n \right) +
\left( 529\,n+336+193\,{n}^{2} \right) f \left( n+1 \right) + \left(
96+63\,n+9\,{n}^{2} \right) f \left( n+2 \right) + \left( -264-205\,n-
37\,{n}^{2} \right) f \left( n+3 \right) + \left( -34\,n-72-4\,{n}^{2}
\right) f \left( n+4 \right) =0,f \left( 0 \right) =0,f \left( 1
\right) =1,f \left( 2 \right) =0,f \left( 3 \right) =1 \right\}
other formats
3.3. Asymptotics
4. Ordinary generating function
\displaystyle
{\rm RootOf} \left( -{\rm \_Z}+x+{{\rm \_Z}}^{2}x+{{\rm \_Z}}^{3}x
\right)
other formats
It satisfies the following differential equation of order 2:
\displaystyle
\left\{ 2\,x+6+ \left( 6\,x+18 \right) y \left( x \right) + \left( 558
\,{x}^{4}+336\,{x}^{3}+36\,{x}^{2}-20\,x-6 \right) {\frac {d}{dx}}y
\left( x \right) + \left( 279\,{x}^{5}+193\,{x}^{4}+9\,{x}^{3}-37\,{x}
^{2}-4\,x \right) {\frac {d^{2}}{d{x}^{2}}}y \left( x \right) =0,y
\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).