 | ECS #63: Trees |
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1. Description
Unlabelled trees of height 4
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Prod} \left( Z,{\rm Set} \left( {\rm T1} \right)
\right) ,{\rm T1}={\rm Prod} \left( Z,{\rm Set} \left( {\rm T2}
\right) \right) ,{\rm T2}={\rm Prod} \left( Z,{\rm Set} \left( {\rm
T3} \right) \right) ,{\rm T3}={\rm Prod} \left( Z,{\rm Set} \left( {
\rm T4} \right) \right) ,{\rm T4}=Z \right\}
other formats
3. Coefficients
3.1. First terms
4. Ordinary generating function
\displaystyle
x{{\rm e}^{\sum _{j_{{1}}=1}^{\infty } \left( {x}^{j_{{1}}}{{\rm e}^{
\sum _{j_{{2}}=1}^{\infty } \left( \left( {x}^{j_{{1}}} \right) ^{j_{{
2}}}{{\rm e}^{\sum _{j_{{3}}=1}^{\infty } \left( \left( \left( {x}^{j
_{{1}}} \right) ^{j_{{2}}} \right) ^{j_{{3}}}{{\rm e}^{\sum _{j_{{4}}=1
}^{\infty }{\frac { \left( \left( \left( {x}^{j_{{1}}} \right) ^{j_{{
2}}} \right) ^{j_{{3}}} \right) ^{j_{{4}}}}{j_{{4}}}}}}{j_{{3}}}^{-1}
\right) }}{j_{{2}}}^{-1} \right) }}{j_{{1}}}^{-1} \right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).