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Seidel-Entringer-Arnold Triangle

The Number Triangle consisting of the Entringer Numbers $E_{n,k}$ arranged in ``ox-plowing'' order,
$E_{10}\rightarrow E_{11}$
$E_{22}\leftarrow E_{21}\leftarrow E_{20}$
$E_{30}\rightarrow E_{31}\rightarrow E_{32}\rightarrow E_{33}$
$E_{44}\leftarrow E_{43}\leftarrow E_{42}\leftarrow E_{41}\leftarrow E_{40}$
$0\rightarrow 1$
$1\leftarrow 1\leftarrow 0$
$0\rightarrow 1\rightarrow 2\rightarrow 2$
$5\leftarrow 5\leftarrow 4\leftarrow 2\leftarrow 0$

See also Bell Number, Boustrophedon Transform, Clark's Triangle, Entringer Number, Euler's Triangle, Leibniz Harmonic Triangle, Number Triangle, Pascal's Triangle


Arnold, V. I. ``Bernoulli-Euler Updown Numbers Associated with Function Singularities, Their Combinatorics, and Arithmetics.'' Duke Math. J. 63, 537-555, 1991.

Arnold, V. I. ``Snake Calculus and Combinatorics of Bernoulli, Euler, and Springer Numbers for Coxeter Groups.'' Russian Math. Surveys 47, 3-45, 1992.

Conway, J. H. and Guy, R. K. In The Book of Numbers. New York: Springer-Verlag, 1996.

Dumont, D. ``Further Triangles of Seidel-Arnold Type and Continued Fractions Related to Euler and Springer Numbers.'' Adv. Appl. Math. 16, 275-296, 1995.

Entringer, R. C. ``A Combinatorial Interpretation of the Euler and Bernoulli Numbers.'' Nieuw. Arch. Wisk. 14, 241-246, 1966.

Millar, J.; Sloane, N. J. A.; and Young, N. E. ``A New Operation on Sequences: The Boustrophedon Transform.'' J. Combin. Th. Ser. A 76, 44-54, 1996.

Seidel, I. ``Über eine einfache Entstehungsweise der Bernoullischen Zahlen und einiger verwandten Reihen.'' Sitzungsber. Münch. Akad. 4, 157-187, 1877.

© 1996-9 Eric W. Weisstein