A000661 Shifts 2 places left under boustrophedon transform.

1, 0, 1, 1, 2, 6, 17, 62, 259, 1230, 6592, 39313, 258575, 1860318, 14538245, 122670593, 1111715644, 10771412394, 111125142979, 1216309735378, 14078811306851, 171837279141312, 2205768169095338, 29707098687614285

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• eigen

References

• G. W. Hill, Acta Mathematica, VIII (1886).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..480
• 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 (Abstract, pdf, ps).
• N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
• N. J. A. Sloane, Transforms.
• Index entries for sequences related to boustrophedon transform

Programs

Mathematica

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 *)

Formula

E.g.f. satisfies: A''(x) - (sec(x)+tan(x))*A(x) = 0 [G. W. Hill, 1886]. - Sergei N. Gladkovskii, Jun 12 2015

a(n) ~ n! * c * 2^n / (n^2 * Pi^n), where c = 21.874759697041762375842937403900898702204499795794357035182354071514... . - Vaclav Kotesovec, Jun 12 2015