 | ECS #415 |
| Introduction | Examples | Search | Submit | Help | Links |
1. Description
No description available
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( C,1\leq {\rm card} \right) ,C={\rm
Prod} \left( Z,S,S \right) ,S={\rm Sequence} \left( B \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ \left( 4\,n+8\,{n}^{2} \right) f \left( n \right) + \left( -
180-354\,n-162\,{n}^{2} \right) f \left( n+1 \right) + \left( 2250+1831
\,n+371\,{n}^{2} \right) f \left( n+2 \right) + \left( -260\,n-420-40\,
{n}^{2} \right) f \left( n+3 \right) =0,f \left( 0 \right) =1,f \left(
1 \right) =1,f \left( 2 \right) =4 \right\}
other formats
3.3. Asymptotics
4. Ordinary generating function
\displaystyle
{\rm RootOf} \left( -{\rm \_Z}+1+2\,x{{\rm \_Z}}^{3}-x{{\rm \_Z}}^{2}
\right)
other formats
It satisfies the following differential equation of order 2:
\displaystyle
\left\{ -2\,x-12+ \left( 12\,x+72 \right) y \left( x \right) + \left(
12\,{x}^{3}-192\,{x}^{2}+718\,x-60 \right) {\frac {d}{dx}}y \left( x
\right) + \left( 8\,{x}^{4}-162\,{x}^{3}+371\,{x}^{2}-40\,x \right) {
\frac {d^{2}}{d{x}^{2}}}y \left( x \right) =0,y \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).