A292758 Expansion of e.g.f. (tan x + sec x)^3.

1, 3, 9, 30, 117, 528, 2709, 15600, 99657, 699648, 5355009, 44382720, 396019197, 3785146368, 38583663309, 417826928640, 4790367838737, 57967904882688, 738337496799609, 9873907221135360, 138327377598038277, 2025896274960580608, 30959719452721035909, 492827536493909114880

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. A000111, A001250.

Programs

Mathematica

nmax = 20; CoefficientList[Series[(Tan[x]+Sec[x])^3, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 02 2019 *)

Formula

a(n) ~ 2^(n + 11/2) * n^(n + 5/2) / (Pi^(n + 5/2) * exp(n)). - Vaclav Kotesovec, Jun 02 2019