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Expansion of e.g.f. log(sech(x) + arctanh(x)).
0

%I #8 Aug 01 2018 22:05:27

%S 0,1,-2,7,-24,173,-1280,11779,-120960,1474969,-19695232,296068991,

%T -4847011840,87094091589,-1687646744576,35308668668155,

%U -789939274514432,18872654969343537,-478658276989173760

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

%F E.g.f.: log(sech(x)+arctanh(x)).

%e x - 2/2!*x^2 + 7/3!*x^3 - 24/4!*x^4 + 173/5!*x^5 ...

%o (PARI) a(n)=local(y); if(n<0,0,y=x+x*O(x^n); n!*polcoeff(log(1/cosh(y)+atanh(y)),n))

%K sign

%O 1,3

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

%E a(0)=0 inserted and title improved by _Sean A. Irvine_, Aug 01 2018