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1. Description
Sum of nth powers
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ S={\rm Union} \left( {\rm Sequence} \left( Z \right) ,{\rm
Sequence} \left( {\rm Union} \left( Z,Z \right) \right) ,{\rm Sequence
} \left( {\rm Union} \left( Z,Z,Z \right) \right) ,{\rm Sequence}
\left( {\rm Union} \left( Z,Z,Z,Z \right) \right) ,{\rm Sequence}
\left( {\rm Union} \left( Z,Z,Z,Z,Z \right) \right) \right)
\right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ -120\,f \left( n \right) +154\,f \left( n+1 \right) -71\,f
\left( n+2 \right) +14\,f \left( n+3 \right) -f \left( n+4 \right) +24
=0,f \left( 0 \right) =5,f \left( 1 \right) =15,f \left( 2 \right) =55,
f \left( 3 \right) =225,f \left( 4 \right) =979 \right\}
other formats
3.3. Closed form
\displaystyle
1+{2}^{n}+{5}^{n}+{3}^{n}+{4}^{n}
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
-{\frac {5+255\,{x}^{2}-450\,{x}^{3}+274\,{x}^{4}-60\,x}{ \left( -1+4\,
x \right) \left( -1+x \right) \left( -1+2\,x \right) \left( -1+3\,x
\right) \left( -1+5\,x \right) }}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).