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%I
%S 1,2,4,9,24,77,294,1309,6664,38177,243034,1701909,13001604,107601977,
%T 959021574,9157981309,93282431344,1009552482977,11568619292914,
%U 139931423833509,1781662223749884,23819069385695177
%N Boustrophedon transform of all-1's sequence.
%C Fill in a triangle, like Pascal's triangle, beginning each row with a 1 and filling in rows alternately right to left and left to right. Thus:
%C ...............1.............
%C ............1..->..2..........
%C .........4..<-.3...<-..1......
%C ......1..->.5..->..8...->..9..
%C ..............................
%D L. Seidel, Ueber eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187.
%H T. D. Noe, <a href="/A000667/b000667.txt">Table of n, a(n) for n=0..100</a>
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>
%H 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://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F E.g.f.: exp(x) (tan x + sec x).
%F Lim n->infinity 2*n*a(n-1)/a(n) = Pi; lim n->infinity a(n)*a(n-2)/a(n-1)^2 = 1 + 1/(n-1) - _Gerald McGarvey_, Aug 13 2004
%F a(n) = Sum_{k, k>=0} binomial(n, k)*A000111(n-k) . a(2n) = A000795(n) + A009747(n), a(2n+1) = A002084(n) + A003719(n) . - _Philippe DELEHAM_, Aug 28 2005
%t With[{nn=30},CoefficientList[Series[Exp[x](Tan[x]+Sec[x]),{x,0,nn}], x]Range[0,nn]!] (* From Harvey P. Dale, Nov 28 2011 *)
%o (Sage) # Algorithm of L. Seidel (1877)
%o def A000667_list(n) :
%o R = []; A = {-1:0, 0:0}
%o k = 0; e = 1
%o for i in range(n) :
%o Am = 1
%o A[k + e] = 0
%o e = -e
%o for j in (0..i) :
%o Am += A[k]
%o A[k] = Am
%o k += e
%o # print [A[z] for z in (-i//2..i//2)]
%o R.append(A[e*i//2])
%o return R
%o A000667_list(10) # _Peter Luschny_, June 02 2012
%Y Absolute value of pairwise sums of A009337.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_, _Simon Plouffe_
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