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 A006217 Number of down-up permutations of n+5 starting with 5. (Formerly M3869) 0
 5, 16, 56, 224, 1024, 5296, 30656, 196544, 1383424, 10608976, 88057856, 786632864, 7525556224, 76768604656, 831846342656, 9541952653184, 115516079079424, 1471865234248336, 19689636672045056, 275914012819601504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Entringer numbers. REFERENCES R. C. Entringer, A combinatorial interpretation of the Euler and Bernoulli numbers, Nieuw Archief voor Wiskunde, 14 (1966), 241-246. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS B. Bauslaugh and F. Ruskey, Generating alternating permutations lexicographically, Nordisk Tidskr. Informationsbehandling (BIT) 30 (1990), 16-26. J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A (1996), 44-54 (Abstract, pdf, ps). C. Poupard, De nouvelles significations énumeratives des nombres d'Entringer, Discrete Math., 38 (1982), 265-271. FORMULA a(0) = 5 and a(n) = 4*E(n+3) - 4*E(n+1) for n >= 1, where E(j) = A000111(j) = j!*[x^j](sec(x) + tan(x)) are the up/down or Euler numbers. - Emeric Deutsch, May 15 2004 EXAMPLE a(0)=5 because we have 51324, 51423, 52314, 52413 and 53412. MAPLE 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); PROG (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])}; /* Michael Somos, Feb 03 2004 */ CROSSREFS Column k=4 in A008282. Cf. A000111. Sequence in context: A153366 A057553 A226973 * A281870 A116914 A047103 Adjacent sequences:  A006214 A006215 A006216 * A006218 A006219 A006220 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Emeric Deutsch, May 15 2004 STATUS approved

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Last modified September 18 20:10 EDT 2021. Contains 347534 sequences. (Running on oeis4.)