A013435 - OEIS

%I #32 Aug 07 2018 03:35:34

%S 0,1,15,495,29015,2666475,354343275,64361872575,15331195839375,

%T 4639834754377875,1739923436670397875,792214640482949058375,

%U 430673843640390204684375,275621285783640234105646875,205164378528197702536594546875,175791115887829825909515376359375

%N E.g.f.: arcsinh(arctanh(x) - arcsin(x)) (odd powers only).

%H Robert Israel, <a href="/A013435/b013435.txt">Table of n, a(n) for n = 0..224</a>

%e 0*x^1 + (1/3!)*x^3 + (15/5!)*x^5 + (495/7!)*x^7 + (29015/9!*x^9) + ...

%p E:= arcsinh(arctanh(x)-arcsin(x)):

%p S:= series(E,x,32):

%p seq(coeff(S,x,k)*k!, k=1..31, 2); # _Robert Israel_, Aug 07 2018

%t With[{nn=30},Join[{0},Take[CoefficientList[Series[-ArcSinh[ArcSin[x]- ArcTanh[x]],{x,0,nn}],x]Range[0,nn-1]!,{6,-1,2}]]] (* _Harvey P. Dale_, Jul 20 2012 *)

%t Union[Range[0, 31]! CoefficientList[ Series[ArcSinh[ArcTanh[x] - ArcSin[x]], {x, 0, 31}], x]] (* _Robert G. Wilson v_, Aug 06 2018 *)

%o (PARI)

%o x='x+O('x^66);

%o egf=asinh(atanh(x)-asin(x));

%o v=Vec(serlaplace(egf));

%o v=vector(#v\2, n, if(n==1, 0, v[2*n-1]))

%o /* _Joerg Arndt_, Jul 20 2012 */

%K nonn

%O 0,3

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

%E Definition corrected by _Harvey P. Dale_, Jul 20 2012

%E Missing a(1)=1 inserted and offset corrected by _Sean A. Irvine_, Aug 06 2018