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A013200 Expansion of e.g.f. log(sec(x)+arctanh(x)). 1

%I #14 Mar 09 2023 04:20:02

%S 0,1,0,1,0,13,-48,677,-4480,54937,-471680,6248713,-65916928,988579109,

%T -12514310144,212756765101,-3159842455552,60179200959793,

%U -1026648500830208,21632158018229009,-416691460525064192

%N Expansion of e.g.f. log(sec(x)+arctanh(x)).

%H Robert Israel, <a href="/A013200/b013200.txt">Table of n, a(n) for n = 0..445</a>

%e E.g.f. = x+1/3!*x^3+13/5!*x^5-48/6!*x^6+677/7!*x^7...

%p S:= series(ln(sec(x)+arctanh(x)), x, 51):

%p seq(coeff(S,x,n)*n!, n=0..50); # _Robert Israel_, Mar 08 2023

%t With[{nn=20},CoefficientList[Series[Log[Sec[x]+ArcTanh[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 21 2014 *)

%o (PARI) my(x='x+O('x^30)); concat(0, Vec(serlaplace(log(1/cos(x)+atanh(x))))) \\ _Michel Marcus_, Mar 08 2023

%K sign

%O 0,6

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

%E Zero prepended to terms by _Harvey P. Dale_, Jan 21 2014

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)