A009707 Expansion of e.g.f. tan(tan(x)*x) (even powers only).

0, 2, 8, 336, 15616, 1450240, 185032704, 33566984192, 7971973332992, 2424984197529600, 915532582868746240, 420569934453637906432, 230845747512083447021568, 149228982402223336708898816

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000182, A003718, A009752, A024265.

Programs

Mathematica

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 *)

Formula

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

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.