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A010094 Triangle of Euler-Bernoulli or Entringer numbers. 6

%I

%S 1,1,1,1,2,2,1,5,5,4,2,16,16,14,10,5,61,61,56,46,32,16,272,272,256,

%T 224,178,122,61,1385,1385,1324,1202,1024,800,544,272,7936,7936,7664,

%U 7120,6320,5296,4094,2770,1385,50521,50521,49136,46366,42272,36976,30656,23536,15872,7936,353792

%N Triangle of Euler-Bernoulli or Entringer numbers.

%D B. Bauslaugh and F. Ruskey, Generating alternating permutations lexicographically, Nordisk Tidskr. Informationsbehandling (BIT) 30 16-26 1990.

%D R. C. Entringer, A combinatorial interpretation of the Euler and Bernoulli numbers, Nieuw Archief voor Wiskunde, 14 (1966), 241-246.

%D Dominique Foata and Guo-Niu Han, Seidel Triangle Sequences and Bi-Entringer Numbers, November 20, 2013; http://www-irma.u-strasbg.fr/~foata/paper/pub123Seidel.pdf

%D C. Poupard, De nouvelles significations enumeratives des nombres d'Entringer, Discrete Math., 38 (1982), 265-271.

%H Vincenzo Librandi, <a href="/A010094/b010094.txt">Rows n = 0..100, flattened</a>

%H D. Foata and G.-N. Han, <a href="http://arxiv.org/abs/1304.2485">Secant Tree Calculus</a>, arXiv preprint arXiv:1304.2485, 2013

%H M. Josuat-Verges, J.-C. Novelli and J.-Y. Thibon, <a href="http://arxiv.org/abs/1110.5272">The algebraic combinatorics of snakes</a>, arXiv preprint arXiv:1110.5272, 2011

%H 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://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 2, 2;

%e 1, 5, 5, 4;

%e 2, 16, 16, 14, 10;

%e 5, 61, 61, 56, 46, 32;

%e 16, 272, 272, 256, 224, 178, 122;

%e 61, 1385, 1385, 1324, 1202, 1024, 800, 544;

%e 272, 7936, 7936, 7664, 7120, 6320, 5296, 4094, 2770; etc.

%e - _Vincenzo Librandi_, Aug 13 2013

%t e[0, 0] = 1; e[_, 0] = 0; e[n_, k_] := e[n, k] = e[n, k-1] + e[n-1, n-k]; Join[{1}, Table[e[n, k], {n, 0, 11}, {k, n, 1, -1}] // Flatten] (* _Jean-Fran├žois Alcover_, Aug 13 2013 *)

%Y Cf. A008282.

%K nonn,tabl,easy,nice,changed

%O 0,5

%A _N. J. A. Sloane_.

%E More terms from Will Root (crosswind(AT)bright.net), Oct 08 2001

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Last modified October 24 23:00 EDT 2014. Contains 248516 sequences.