%I A006217 M3869
%S A006217 5,16,56,224,1024,5296,30656,196544,1383424,10608976,88057856,786632864,
%T A006217 7525556224,76768604656,831846342656,9541952653184,115516079079424,
%U A006217 1471865234248336,19689636672045056,275914012819601504
%N A006217 Number of down-up permutations of n+5 starting with 5.
%C A006217 Entringer numbers.
%D A006217 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006217 R. C. Entringer, A combinatorial interpretation of the Euler and Bernoulli 
               numbers, Nieuw Archief voor Wiskunde, 14 (1966), 241-246.
%D A006217 C. Poupard, De nouvelles significations enumeratives des nombres d'Entringer, 
               Discrete Math., 38 (1982), 265-271.
%H A006217 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 
               (<a href="http://www.research.att.com/~njas/doc/bous.txt">Abstract</
               a>, <a href="http://www.research.att.com/~njas/doc/bous.pdf">pdf</
               a>, <a href="http://www.research.att.com/~njas/doc/bous.ps">ps</a>
               ).
%H A006217 B. Bauslaugh and F. Ruskey, <a href="http://www.cs.uvic.ca/~fruskey/Publications/
               ">Generating alternating permutations lexicographically</a>, Nordisk 
               Tidskr. Informationsbehandling (BIT) 30 16-26 1990.
%F A006217 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
%e A006217 a(0)=5 because we have 51324, 51423, 52314, 52413 and 53412.
%p A006217 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);
%o A006217 (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)
%Y A006217 Column k=4 in A008282.
%Y A006217 Cf. A000111.
%Y A006217 Sequence in context: A120343 A153366 A057553 this_sequence A116914 A047103 
               A077235
%Y A006217 Adjacent sequences: A006214 A006215 A006216 this_sequence A006218 A006219 
               A006220
%K A006217 nonn,easy
%O A006217 0,1
%A A006217 N. J. A. Sloane (njas(AT)research.att.com).
%E A006217 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 15 2004