OFFSET
0,1
COMMENTS
Entringer numbers.
REFERENCES
R. C. Entringer, A combinatorial interpretation of the Euler and Bernoulli numbers, Nieuw Archief voor Wiskunde, 14 (1966), 241-246.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
B. Bauslaugh and F. Ruskey, Generating alternating permutations lexicographically, Nordisk Tidskr. Informationsbehandling (BIT) 30 (1990), 16-26.
J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996), 44-54 (Abstract, pdf, ps).
C. Poupard, De nouvelles significations énumeratives des nombres d'Entringer, Discrete Math., 38 (1982), 265-271.
FORMULA
a(0) = 5 and a(n) = 4*E(n+3) - 4*E(n+1) for n >= 1, where E(j) = A000111(j) = j!*[x^j](sec(x) + tan(x)) are the up/down or Euler numbers. - Emeric Deutsch, May 15 2004
EXAMPLE
a(0)=5 because we have 51324, 51423, 52314, 52413 and 53412.
MAPLE
f:=sec(x)+tan(x): fser:=series(f, x=0, 35): E[0]:=1: for n from 1 to 40 do E[n]:=n!*coeff(fser, x^n) od: 5, seq(4*E[n-1]-4*E[n-3], n=5..23);
PROG
(PARI) {a(n) = local(v=[1], t); if( n<0, 0, for(k=2, n+5, t=0; v = vector(k, i, if( i>1, t += v[k+1-i]))); v[5])}; /* Michael Somos, Feb 03 2004 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, May 15 2004
STATUS
approved