Search: id:A008280
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%I A008280
%S A008280 1,0,1,1,1,0,0,1,2,2,5,5,4,2,0,0,5,10,14,16,16,61,61,56,46,
%T A008280 32,16,0,0,61,122,178,224,256,272,272,1385,1385,1324,1202,
%U A008280 1024,800,544,272,0,0,1385,2770,4094,5296,6320,7120,7664
%N A008280 Boustrophedon version of triangle of Euler-Bernoulli or Entringer numbers 
               read by rows.
%C A008280 The earliest known reference for this triangle is Seidel (1877). - D. 
               E. Knuth, Jul 13 2007
%D A008280 Arnold, V. I., Bernoulli-Euler updown numbers associated with function 
               singularities, their combinatorics and arithmetics, Duke Math. J. 
               63 (1991), 537-555.
%D A008280 V. I. Arnold, The calculus of snakes and the combinatorics of Bernoulli, 
               Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., 
               47 (#1, 1992), 3-45 = Russian Math. Surveys, Vol. 47 (1992), 1-51.
%D A008280 M. D. Atkinson: Zigzag permutations and comparisons of adjacent elements, 
               Information Processing Letters 21 (1985), 187-189.
%D A008280 M. D. Atkinson: Partial orders and comparison problems, Sixteenth Southeastern 
               Conference on Combinatorics, Graph Theory and Computing, (Boca Raton, 
               Feb 1985), Congressus Numerantium 47, 77-88.
%D A008280 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 
               1996, p. 110.
%D A008280 A. J. Kempner, On the shape of polynomial curves, Tohoku Math. J., 37 
               (1933), 347-362.
%D A008280 C. Poupard, De nouvelles significations enumeratives des nombres d'Entringer, 
               Discrete Math., 38 (1982), 265-271.
%D A008280 L. Seidel, Ueber eine einfache Entstehungsweise der Bernoulli'schen Zahlen 
               und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen 
               Classe der k\"oniglich bayerischen Akademie der Wissenschaften zu 
               M\"unchen, volume 7 (1877), 157-187.
%H A008280 B. Gourevitch, <a href="http://www.pi314.net">L'univers de Pi</a>
%H A008280 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: 
               the Boustrophedon on transform, J. Combin. Theory, 17A 44-54 1996 
               (<a href="http://www.research.att.com/~njas/doc/bous.txt">Abstract</
               a>, <a href="http://www.research.att.com/~njas/doc/bous.pdf">pdf</
               a>, <a href="http://www.research.att.com/~njas/doc/bous.ps">ps</a>
               ).
%H A008280 R. Street, <a href="http://arXiv.org/abs/math.HO/0303267">Trees, permutations 
               and the tangent function</a>
%e A008280 This version of the triangle begins:
%e A008280 .............1
%e A008280 ...........0...1
%e A008280 .........1...1...0
%e A008280 .......0...1...2...2
%e A008280 .....5...5...4...2...0
%e A008280 ...0...5..10..14..16..16
%e A008280 See A008281 and A108040 for other versions.
%Y A008280 Cf. A008281.
%Y A008280 Sequence in context: A045537 A161622 A116559 this_sequence A063960 A025510 
               A158106
%Y A008280 Adjacent sequences: A008277 A008278 A008279 this_sequence A008281 A008282 
               A008283
%K A008280 nonn,tabl,nice
%O A008280 0,9
%A A008280 N. J. A. Sloane (njas(AT)research.att.com).

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