A013422 - OEIS

%I #14 Mar 06 2013 12:20:12

%S 0,3,-7,497,10649,955757,167741741,20817188849,5637483533393,

%T 1653225944489237,560689820639903957,269465649695982142009,

%U 138258119776900090716601,87774869737967098700912797,65239835100565334768577561149,54460490625029012562328972397057

%N E.g.f.: arcsin(arcsin(x)-tanh(x)) (odd coefficients only).

%H Alois P. Heinz, <a href="/A013422/b013422.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = (2n+1) * [x^(2n+1)] arcsin(arcsin(x)-tanh(x)).

%e arcsin(arcsin(x)-tanh(x)) = 3/3!*x^3-7/5!*x^5+497/7!*x^7+10649/9!*x^9... .

%p egf:= arcsin(arcsin(x)-tanh(x)):

%p a:= n-> (2*n+1)!*coeff(series(egf, x, 2*n+3),x,(2*n+1)):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Mar 06 2013

%t With[{nn=30},Take[CoefficientList[Series[ArcSin[ArcSin[x]-Tanh[x]],{x,0,nn}],x]Range[0,nn-1]!,{2,-1,2}]] (* _Harvey P. Dale_, Mar 06 2013 *)

%K sign

%O 0,2

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

%E More terms from _Harvey P. Dale_, Mar 06 2013