 | ECS #416 |
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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( C,C,Z \right) ,C={\rm Sequence} \left( S
\right) ,S={\rm Sequence} \left( B,1\leq {\rm card} \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( -10\,n+20\,{n}^{2} \right) f \left( n \right) +
\left( -96-395\,n-371\,{n}^{2} \right) f \left( n+1 \right) + \left(
1152+1236\,n+324\,{n}^{2} \right) f \left( n+2 \right) + \left( -176\,n
-240-32\,{n}^{2} \right) f \left( n+3 \right) =0,f \left( 0 \right) =0,
f \left( 1 \right) =1,f \left( 2 \right) =3 \right\}
other formats
3.3. Asymptotics
4. Ordinary generating function
\displaystyle
2\, \left( {\rm RootOf} \left( -{\rm \_Z}+1+2\,{{\rm \_Z}}^{3}x-{{\rm
\_Z}}^{2}x \right) \right) ^{2}x-{\rm RootOf} \left( -{\rm \_Z}+1+2\,{
{\rm \_Z}}^{3}x-{{\rm \_Z}}^{2}x \right) x
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It satisfies the following differential equation of order 2:
\displaystyle
\left\{ \left( -72\,x-24 \right) y \left( x \right) + \left( -24\,{x}
^{2}+10\,{x}^{3}+264\,x-16 \right) {\frac {d}{dx}}y \left( x \right) +
\left( 20\,{x}^{4}-371\,{x}^{3}+324\,{x}^{2}-32\,x \right) {\frac {d^{
2}}{d{x}^{2}}}y \left( x \right) +48\,x+16=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).