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A006215
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Number of down-up permutations of n+6 starting with n+1.
(Formerly M5007)
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0
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0, 16, 122, 800, 5296, 36976, 275792, 2204480, 18870016, 172585936, 1681843712, 17411416160, 190939611136, 2211961358896, 26999750469632, 346419349043840
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Entringer numbers.
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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).
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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).
Index entries for sequences related to tournaments
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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
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EXAMPLE
| a(1)=16 because we have 2143657, 2143756, 2153647, 2153746, 2154637, 2154736, 2163547, 2163745, 2164537, 2164735, 2165734, 2173546, 2173645, 2174536, 2174635 and 2175634.
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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);
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CROSSREFS
| Cf. A000111, A008282.
Sequence in context: A053883 A191484 A030508 * A060633 A125353 A126511
Adjacent sequences: A006212 A006213 A006214 * A006216 A006217 A006218
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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