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A006217 Number of down-up permutations of n+5 starting with 5.
(Formerly M3869)
0
5, 16, 56, 224, 1024, 5296, 30656, 196544, 1383424, 10608976, 88057856, 786632864, 7525556224, 76768604656, 831846342656, 9541952653184, 115516079079424, 1471865234248336, 19689636672045056, 275914012819601504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Entringer numbers.

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..19.

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).

FORMULA

a(0)=5, a(n)=4E(n+3)-4E(n+1) (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

Column k=4 in A008282.

Cf. A000111.

Sequence in context: A153366 A057553 A226973 * A281870 A116914 A047103

Adjacent sequences:  A006214 A006215 A006216 * A006218 A006219 A006220

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Emeric Deutsch, May 15 2004

STATUS

approved

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Last modified January 20 15:25 EST 2019. Contains 319333 sequences. (Running on oeis4.)