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Search: id:A006217
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| A006217 |
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Number of down-up permutations of n+5 starting with 5.
(Formerly M3869)
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+0
1
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| 5, 16, 56, 224, 1024, 5296, 30656, 196544, 1383424, 10608976, 88057856, 786632864, 7525556224, 76768604656, 831846342656, 9541952653184, 115516079079424, 1471865234248336, 19689636672045056, 275914012819601504
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Entringer numbers.
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REFERENCES
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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.
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LINKS
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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).
B. Bauslaugh and F. Ruskey, Generating alternating permutations lexicographically, Nordisk Tidskr. Informationsbehandling (BIT) 30 16-26 1990.
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FORMULA
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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 (deutsch(AT)duke.poly.edu), May 15 2004
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EXAMPLE
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a(0)=5 because we have 51324, 51423, 52314, 52413 and 53412.
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MAPLE
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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);
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PROGRAM
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(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]) (from Michael Somos)
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CROSSREFS
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Column k=4 in A008282.
Cf. A000111.
Sequence in context: A120343 A153366 A057553 this_sequence A116914 A047103 A077235
Adjacent sequences: A006214 A006215 A006216 this_sequence A006218 A006219 A006220
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2004
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