A292757 Expansion of e.g.f. exp(x)*(1+tan(x))/((1-tan(x))*(tan(x)+sec(x))).

1, 2, 4, 15, 72, 467, 3534, 31675, 321832, 3692927, 46988914, 658330035, 10056866292, 166476324887, 2967375285294, 56673879465595, 1154538708267952, 24990204586402847, 572731801523141674, 13855288923332516355, 352821804274904668812, 9433763230045116440807, 264251645557758720762054

Offset: 0

Author

N. J. A. Sloane, Sep 26 2017

Keywords

• nonn

Links

• C. K. Cook, M. R. Bacon, and R. A. Hillman, Higher-order Boustrophedon transforms for certain well-known sequences, Fib. Q., 55(3) (2017), 201-208.

Crossrefs

Cf. A000834.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Exp[x]*(1+Tan[x])/((1-Tan[x])*(Tan[x]+Sec[x])), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 02 2019 *)

Formula

a(n) ~ 2^(2*n + 3) * n^(n + 1/2) / ((2 + sqrt(2)) * Pi^(n + 1/2) * exp(n - Pi/4)). - Vaclav Kotesovec, Jun 02 2019