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A010094 Triangle of Euler-Bernoulli or Entringer numbers. 6
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, 224, 178, 122, 61, 1385, 1385, 1324, 1202, 1024, 800, 544, 272, 7936, 7936, 7664, 7120, 6320, 5296, 4094, 2770, 1385, 50521, 50521, 49136, 46366, 42272, 36976, 30656, 23536, 15872, 7936, 353792 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

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

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

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

LINKS

Vincenzo Librandi, Rows n = 0..100, flattened

D. Foata and G.-N. Han, Secant Tree Calculus, arXiv preprint arXiv:1304.2485, 2013

Dominique Foata and Guo-Niu Han, Seidel Triangle Sequences and Bi-Entringer Numbers, November 20, 2013.

M. Josuat-Verges, J.-C. Novelli and J.-Y. Thibon, The algebraic combinatorics of snakes, arXiv preprint arXiv:1110.5272, 2011

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 (Abstract, pdf, ps).

EXAMPLE

Triangle begins:

    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,  224,  178,  122;

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

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

  - Vincenzo Librandi, Aug 13 2013

MATHEMATICA

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 *)

CROSSREFS

Cf. A008282.

Sequence in context: A123158 A185414 A133611 * A019710 A118806 A171670

Adjacent sequences:  A010091 A010092 A010093 * A010095 A010096 A010097

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified February 23 11:04 EST 2018. Contains 299536 sequences. (Running on oeis4.)