A013463 E.g.f.: sin(arctan(x) - arctanh(x)) (odd powers only).

0, -4, 0, -1440, 17920, -7257600, 395366400, -175791616000, 24049778688000, -13090802909184000, 3482386518507520000, -2338795470534082560000, 1043344639170183168000000, -855872901958901432320000000

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