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DLMF:24.6.E5
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Formula:8162
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MaRDI QID
Q8162
Label: DLMF:24.6.E5
Digital Library of Mathematical Functions ID
24.6.E5
E
2
n
=
1
2
n
-
1
∑
k
=
0
n
-
1
(
-
1
)
n
-
k
(
n
-
k
)
2
n
∑
j
=
0
k
(
2
n
-
2
j
k
-
j
)
2
j
,
Euler-number-E
2
𝑛
1
superscript
2
𝑛
1
superscript
subscript
𝑘
0
𝑛
1
superscript
1
𝑛
𝑘
superscript
𝑛
𝑘
2
𝑛
superscript
subscript
𝑗
0
𝑘
binomial
2
𝑛
2
𝑗
𝑘
𝑗
superscript
2
𝑗
{\displaystyle{\displaystyle E_{2n}=\frac{1}{2^{n-1}}\sum_{k=0}^{n-1}(-1)^{n-k% }(n-k)^{2n}\*\sum_{j=0}^{k}{2n-2j\choose k-j}2^{j},}}
Constraint(s)
Symbols List
E
n
Euler-number-E
𝑛
{\displaystyle{\displaystyle E_{\NVar{n}}}}
:
(
m
n
)
binomial
𝑚
𝑛
{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
:
j
𝑗
{\displaystyle{\displaystyle j}}
: integer
k
𝑘
{\displaystyle{\displaystyle k}}
: integer
n
𝑛
{\displaystyle{\displaystyle n}}
: integer
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