A013463 - OEIS

%I #30 Dec 18 2018 11:11:10

%S 0,-4,0,-1440,17920,-7257600,395366400,-175791616000,24049778688000,

%T -13090802909184000,3482386518507520000,-2338795470534082560000,

%U 1043344639170183168000000,-855872901958901432320000000

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

%H Robert Israel, <a href="/A013463/b013463.txt">Table of n, a(n) for n = 0..224</a>

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

%F 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

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

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

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

%p seq((2*k+1)!*coeff(S,x,2*k+1),k=0..30); # _Robert Israel_, Dec 18 2018

%t 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 *)

%K sign

%O 0,2

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

%E Definition clarified by _Harvey P. Dale_, Aug 14 2014

%E Prepended a(0)=0 by _Joerg Arndt_, Aug 19 2014