%I A008281
%S A008281 1,0,1,0,1,1,0,1,2,2,0,2,4,5,5,0,5,10,14,16,16,0,16,32,46,
%T A008281 56,61,61,0,61,122,178,224,256,272,272,0,272,544,800,1024,
%U A008281 1202,1324,1385,1385,0,1385,2770,4094,5296,6320,7120,7664,7936,7936
%N A008281 Triangle of Euler-Bernoulli or Entringer numbers read by rows.
%C A008281 Zig-Zag numbers (see the Conway and Guy reference p. 110 and the J.-P. 
               Delahaye reference, p. 31).
%C A008281 Approximation to Pi: 2*n*a(n-1,n-1)/a(n,n), n>=3. See A132049(n)/A132050(n). 
               See the Delahaye reference, p. 31.
%D A008281 Arnold, V. I., Bernoulli-Euler updown numbers associated with function 
               singularities, their combinatorics and arithmetics, Duke Math. J. 
               63 (1991), 537-555.
%D A008281 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 A008281 J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 
               p. 110.
%D A008281 J.-P. Delahaye, Pi - die Story (German translation), Birkhaeuser, 1999 
               Basel, p. 31. French original: Le fascinant nombre Pi, Pour la Science, 
               Paris, 1997.
%D A008281 C. Poupard, De nouvelles significations enumeratives des nombres d'Entringer, 
               Discrete Math., 38 (1982), 265-271.
%H A008281 B. Gourevitch, <a href="http://www.pi314.net">L'univers de Pi</a>
%H A008281 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>
               ).
%F A008281 a(0,0)=1, a(n,m)=0 if n<m, a(n,m)=0 if m<0 else sum(a(n-1,n-k),k=1..m).
%e A008281 This version of the triangle begins:
%e A008281 .............1
%e A008281 ...........0...1
%e A008281 .........0...1...1
%e A008281 .......0...1...2...2
%e A008281 .....0...2...4...5...5
%e A008281 ...0...5..10..14..16..16
%e A008281 See A008280 and A108040 for other versions.
%p A008281 A008281 := proc(h,k) option remember ; if h=1 and k=1 or h=0 then RETURN(1) 
               ; elif h>=1 and k> h then RETURN(0) ; elif h=k then RETURN( A008281(h,
               h-1)) ; else RETURN( add(A008281(h-1,j),j=h-k..h-1) ) ; fi ; end: 
               for h from 0 to 10 do for k from 0 to h do printf("%d, ",A008281(h,
               k)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 
               27 2006
%Y A008281 Cf. A008280.
%Y A008281 Sequence in context: A159916 A159286 A006462 this_sequence A094671 A021458 
               A099064
%Y A008281 Adjacent sequences: A008278 A008279 A008280 this_sequence A008282 A008283 
               A008284
%K A008281 nonn,tabl,nice,easy
%O A008281 0,9
%A A008281 N. J. A. Sloane (njas(AT)research.att.com).