|
Search: id:A006215
|
|
|
| A006215 |
|
Number of down-up permutations of n+6 starting with n+1.
(Formerly M5007)
|
|
+0
1
|
|
| 0, 16, 122, 800, 5296, 36976, 275792, 2204480, 18870016, 172585936, 1681843712, 17411416160, 190939611136, 2211961358896, 26999750469632, 346419349043840
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Entringer numbers.
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
|
B. Bauslaugh and F. Ruskey, Generating alternating permutations lexicographically, Nordisk Tidskr. Informationsbehandling (BIT) 30 16-26 1990.
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).
Index entries for sequences related to tournaments
|
|
FORMULA
|
a(n)=sum((-1)^i*binomial(n, 2i+1)*E[n+4-2i], 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+5, n), where T is the triangle in A008282. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2004
|
|
EXAMPLE
|
a(1)=16 because we have 2143657, 2143756, 2153647, 2153746, 2154637, 2154736, 2163547, 2163745, 2164537, 2164735, 2165734, 2173546, 2173645, 2174536, 2174635 and 2175634.
|
|
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+4-2*i], i=0..floor((n-1)/2)): seq(a(n), n=0..15);
|
|
CROSSREFS
|
Cf. A000111, A008282.
Sequence in context: A068880 A053883 A030508 this_sequence A060633 A125353 A126511
Adjacent sequences: A006212 A006213 A006214 this_sequence A006216 A006217 A006218
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
