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Search: id:A006216
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| A006216 |
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Number of down-up permutations of n+4 starting with 4.
(Formerly M1466)
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+0
1
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| 2, 5, 14, 46, 178, 800, 4094, 23536, 150178, 1053440, 8057774, 66750976, 595380178, 5688903680, 57975175454, 627692271616, 7195247514178, 87056789995520, 1108708685037134, 14825405274259456, 207676251991176178
(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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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).
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FORMULA
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a(n)=3E(n+2)-E(n), 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(1)=5 because we have 41325,41523,42314,42513 and 43512.
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MAPLE
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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: seq(3*E[n+2]-E[n], n=0..20);
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PROGRAM
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(PARI) a(n)=local(v=[1], t); if(n<0, 0, for(k=2, n+4, t=0; v=vector(k, i, if(i>1, t+=v[k+1-i]))); v[4]) (from Michael Somos)
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CROSSREFS
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Cf. A000111. Column k=3 in A008282.
Sequence in context: A149898 A001680 A107268 this_sequence A148337 A149899 A149900
Adjacent sequences: A006213 A006214 A006215 this_sequence A006217 A006218 A006219
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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