A009707 - OEIS

%I #17 Dec 21 2017 17:37:07

%S 0,2,8,336,15616,1450240,185032704,33566984192,7971973332992,

%T 2424984197529600,915532582868746240,420569934453637906432,

%U 230845747512083447021568,149228982402223336708898816

%N Expansion of e.g.f. tan(tan(x)*x) (even powers only).

%H Vaclav Kotesovec, <a href="/A009707/b009707.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ c * d^n * n^(2*n + 1/2) / exp(2*n), where d = 3.9786913954409425781217887822690623430980810... is the root of the equation tan(2/sqrt(d)) = Pi*sqrt(d)/4 and c = 1.4057183994645... - _Vaclav Kotesovec_, Dec 21 2017

%t nmax = 20; Table[(CoefficientList[Series[Tan[x*Tan[x]], {x, 0, 2*nmax}], x] * Range[0, 2 nmax]!)[[n]], {n, 1, 2*nmax + 1, 2}] (* _Vaclav Kotesovec_, Dec 21 2017 *)

%Y Cf. A000182, A003718, A009752, A024265.

%K nonn

%O 0,2

%A _R. H. Hardin_

%E Extended and signs tested Mar 15 1997 by _Olivier Gérard_.