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A000661 Shifts 2 places left under boustrophedon transform.

%I A000661 #24 Feb 01 2022 01:09:28
%S A000661 1,0,1,1,2,6,17,62,259,1230,6592,39313,258575,1860318,14538245,
%T A000661 122670593,1111715644,10771412394,111125142979,1216309735378,
%U A000661 14078811306851,171837279141312,2205768169095338,29707098687614285
%N A000661 Shifts 2 places left under boustrophedon transform.
%D A000661 G. W. Hill, Acta Mathematica, VIII (1886).
%H A000661 Vaclav Kotesovec, <a href="/A000661/b000661.txt">Table of n, a(n) for n = 0..480</a>
%H A000661 J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon 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 A000661 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 A000661 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H A000661 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A000661 E.g.f. satisfies: A''(x) - (sec(x)+tan(x))*A(x) = 0 [G. W. Hill, 1886]. - _Sergei N. Gladkovskii_, Jun 12 2015
%F A000661 a(n) ~ n! * c * 2^n / (n^2 * Pi^n), where c = 21.874759697041762375842937403900898702204499795794357035182354071514... . - _Vaclav Kotesovec_, Jun 12 2015
%t A000661 nmax = 30; sectan = Normal[Series[Sec[x] + Tan[x], {x, 0, nmax+1}]]; Subscript[a,0]=1; Subscript[a,1]=0; egf = Sum[Subscript[a,k]*x^k, {k,0,nmax+1}]; Table[Subscript[a,k]*k!, {k,0,nmax}] /.Solve[Take[CoefficientList[Expand[ sectan*egf - D[egf,{x,2}]],x], nmax-1] == ConstantArray[0, nmax-1]][[1]] (* _Vaclav Kotesovec_, Jun 12 2015 *)
%K A000661 nonn,eigen
%O A000661 0,5
%A A000661 _N. J. A. Sloane_