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A009707 Expansion of e.g.f. tan(tan(x)*x) (even powers only). 4
0, 2, 8, 336, 15616, 1450240, 185032704, 33566984192, 7971973332992, 2424984197529600, 915532582868746240, 420569934453637906432, 230845747512083447021568, 149228982402223336708898816 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

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 *)

CROSSREFS

Cf. A000182, A003718, A009752, A024265.

Sequence in context: A013135 A012999 A013003 * A013176 A220904 A009489

Adjacent sequences:  A009704 A009705 A009706 * A009708 A009709 A009710

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Extended and signs tested Mar 15 1997 by Olivier Gérard.

STATUS

approved

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Last modified May 22 22:13 EDT 2022. Contains 353959 sequences. (Running on oeis4.)