|
| |
|
|
A006214
|
|
Number of down-up permutations of n+5 starting with n+1.
(Formerly M3967)
|
|
0
| |
|
|
0, 5, 32, 178, 1024, 6320, 42272, 306448, 2401024, 20253440, 183194912, 1769901568, 18198049024, 198465167360, 2288729963552, 27831596812288, 355961301697024
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
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
| 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(n)=sum((-1)^i*binomial(n, 2i+1)*E[n+3-2i], i=0..floor((n-1)/2)), where E[j]=A000111(j)=j!*[x^j]((sec(x)+tan(x)) are the up/down or Euler numbers. a(n)=T(n+4, n), where T is the triangle in A008282. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2004
|
|
|
EXAMPLE
| a(1)=5 because we have 214365, 215364, 215463, 216354 and 216453.
|
|
|
MAPLE
| f:=sec(x)+tan(x): fser:=series(f, x=0, 30): E[0]:=1: for n from 1 to 25 do E[n]:=n!*coeff(fser, x^n) od: a:=n->sum((-1)^i*binomial(n, 2*i+1)*E[n+3-2*i], i=0..floor((n-1)/2)): seq(a(n), n=0..16);
|
|
|
CROSSREFS
| Cf. A000111, A008282.
Sequence in context: A001589 A177467 A193783 * A157704 A015541 A024064
Adjacent sequences: A006211 A006212 A006213 * A006215 A006216 A006217
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
