ECS #116
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1. Description

No description available

2. Specification

This labelled structure is specified as S in

\displaystyle \left\{ B={\rm Set} \left( Z \right) ,C={\rm Cycle} \left( Z \right) , S={\rm Prod} \left( C,B \right) \right\}
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3. Coefficients

3.1. First terms

3.2. Recurrence

\displaystyle \left\{ \left( -n-1 \right) f \left( n \right) + \left( 4+2\,n \right) f \left( n+1 \right) + \left( -n-4 \right) f \left( 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\}
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3.3. Closed form

\displaystyle \sum _{{\rm \_n0}=0}^{n-1}{{\rm e}^{1}}\Gamma \left( {\rm \_n0}+1,1 \right)
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3.4. Asymptotics

4. Exponential generating function

\displaystyle \ln \left( - \left( -1+x \right) ^{-1} \right) {{\rm e}^{x}}
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It satisfies the following differential equation of order 2:

\displaystyle \left\{ \left( -2+x \right) y \left( x \right) + \left( 3-2\,x \right) {\frac {d}{dx}}y \left( x \right) + \left( -1+x \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\}
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5. References

EIS A002104

6. Random structure


Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).

Generated: 2009-11-21 09:19:51 in 2. seconds of elapsed time.
Based on commit 9d1e479..., Fri Jul 10 14:52:30 2009 +0200.
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