OFFSET
0,5
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.
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
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 *)
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
STATUS
approved