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Expansion of e.g.f. exp(x)*(tan(x)+sec(x))^2.
3

%I #13 Sep 29 2023 12:01:28

%S 1,3,9,29,105,433,2029,10709,63025,409713,2917749,22599389,189200745,

%T 1702839193,16397919469,168248900069,1832540103265,21118133619873,

%U 256725609081189,3283461599832749,44074814323890585,619564244562907753,9102144892897546909,139495284063955397429

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

%H C. K. Cook, M. R. Bacon, and R. A. Hillman, <a href="https://www.fq.math.ca/Papers1/55-3/CookBaconHillman01222017.pdf">Higher-order Boustrophedon transforms for certain well-known sequences</a>, Fib. Q., 55(3) (2017), 201-208.

%F a(n) ~ 2^(n + 9/2) * n^(n + 3/2) / (Pi^(n + 3/2) * exp(n - Pi/2)). - _Vaclav Kotesovec_, Jun 02 2019

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

%Y Cf. A000667.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Sep 26 2017