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A024265 Expansion of tan(tan(x) * x)/2. 2
0, 1, 4, 168, 7808, 725120, 92516352, 16783492096, 3985986666496, 1212492098764800, 457766291434373120, 210284967226818953216, 115422873756041723510784, 74614491201111668354449408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = A009707(n)/2. - Vaclav Kotesovec, Dec 21 2017

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 = 0.7028591997322... - Vaclav Kotesovec, Dec 21 2017

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[(Tan[Tan[x]*x])/2, {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Nov 03 2015 *)

CROSSREFS

Cf. A009707.

Sequence in context: A159011 A077257 A278124 * A302453 A061710 A262687

Adjacent sequences:  A024262 A024263 A024264 * A024266 A024267 A024268

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Extended and signs tested 03/97.

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Nov 03 2015

STATUS

approved

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Last modified August 16 05:16 EDT 2022. Contains 356162 sequences. (Running on oeis4.)