 | ECS #131 |
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1. Description
No description available
2. Specification
This labelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( C \right) ,C={\rm Prod} \left( B,Z
\right) ,S={\rm Set} \left( C \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -f \left( n \right) + \left( -4\,n-2 \right) f \left( n+1
\right) +f \left( n+2 \right) =0,f \left( 0 \right) =1,f \left( 1
\right) =1 \right\}
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3.3. Asymptotics
4. Exponential generating function
\displaystyle
{{\rm e}^{1/2-1/2\,\sqrt {1-4\,x}}}
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It satisfies the following differential equation of order 2:
\displaystyle
\left\{ y \left( x \right) +2\,{\frac {d}{dx}}y \left( x \right) +
\left( -1+4\,x \right) {\frac {d^{2}}{d{x}^{2}}}y \left( x \right) =0,
y \left( 0 \right) =1,\mbox {D} \left( y \right) \left( 0 \right) =1
\right\}
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5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).