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A013463 E.g.f.: sin(arctan(x) - arctanh(x)) (odd powers only). 1
0, -4, 0, -1440, 17920, -7257600, 395366400, -175791616000, 24049778688000, -13090802909184000, 3482386518507520000, -2338795470534082560000, 1043344639170183168000000, -855872901958901432320000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..224

FORMULA

a(n) = (2*n+1)! * [x^(2*n+1)] sin(arctan(x)-arctanh(x)). - Alois P. Heinz, Aug 20 2014

16*(2*k + 7)*(2*k + 5)*(2*k + 3)*(2*k + 1)*(k + 4)*(k + 2)*(k + 1)^2*a(k) + 16*(k + 2)*(2*k + 5)*(2*k + 7)*(k + 4)*a(k+1) - 8*(2*k + 7)*(2*k + 5)*(k + 2)*(k + 4)*a(k+2) + a(k+4) = 0. - Robert Israel, Dec 18 2018

EXAMPLE

sin(arctan(x) - arctanh(x)) = -4/3!*x^3 -1440/7!*x^7 +17920/9!*x^9 ...

MAPLE

f:= sin(arctan(x)-arctanh(x)):

S:= series(f, x, 62):

seq((2*k+1)!*coeff(S, x, 2*k+1), k=0..30); # Robert Israel, Dec 18 2018

MATHEMATICA

With[{nn=30}, Take[CoefficientList[Series[Sin[ArcTan[x]-ArcTanh[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Aug 14 2014 *)

CROSSREFS

Sequence in context: A216675 A012502 A130105 * A013464 A331582 A306819

Adjacent sequences:  A013460 A013461 A013462 * A013464 A013465 A013466

KEYWORD

sign

AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)

EXTENSIONS

Definition clarified by Harvey P. Dale, Aug 14 2014

Prepended a(0)=0 by Joerg Arndt, Aug 19 2014

STATUS

approved

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Last modified August 12 13:34 EDT 2022. Contains 356077 sequences. (Running on oeis4.)