Entringer Number
 |
(1)
|
The Entringer numbers 
(OEIS A008281)
are the number of permutations of 
, starting
with 
, which, after initially falling, alternately
fall then rise. The Entringer numbers are given by
 |  |  |
(2)
|
 |  |  |
(3)
|
together with the recurrence relation
 |
(4)
|
A suitably arranged number triangle of these numbers is known as the Seidel-Entringer-Arnold triangle.
The numbers 
are the secant
and tangent numbers given by the Maclaurin
series
 |
(5)
|
They have closed form
 |
(6)
|
. where 
is an Euler
number and 
is a Bernoulli
number.
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entringer number