A292756 Expansion of e.g.f. exp(x)*(tan(x)+sec(x))^2.

1, 3, 9, 29, 105, 433, 2029, 10709, 63025, 409713, 2917749, 22599389, 189200745, 1702839193, 16397919469, 168248900069, 1832540103265, 21118133619873, 256725609081189, 3283461599832749, 44074814323890585, 619564244562907753, 9102144892897546909, 139495284063955397429

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. A000667.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Exp[x]*(Tan[x]+Sec[x])^2, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 02 2019 *)

Formula

a(n) ~ 2^(n + 9/2) * n^(n + 3/2) / (Pi^(n + 3/2) * exp(n - Pi/2)). - Vaclav Kotesovec, Jun 02 2019