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Expansion of e.g.f. sinh(log(1+tanh(x))).
2

%I #21 Jan 22 2018 03:05:07

%S 0,1,-1,1,-4,16,-16,-104,-64,4096,-256,-176384,-1024,11186176,-4096,

%T -951870464,-16384,104932704256,-65536,-14544442425344,-262144,

%U 2475749027086336,-1048576,-507711943251329024,-4194304,123460740095112380416,-16777216

%N Expansion of e.g.f. sinh(log(1+tanh(x))).

%H G. C. Greubel, <a href="/A009570/b009570.txt">Table of n, a(n) for n = 0..450</a>

%F E.g.f.: (1/Q(0)-Q(0))/2, where Q(k) = 1 - x/( 2*k+1 + x/Q(k+1) ); (continued fraction). - _Sergei N. Gladkovskii_, Dec 20 2013

%t With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + Tanh[x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jan 21 2018 *)

%o (PARI) x='x+O('x^30); concat([0], Vec(serlaplace( sin(log(1+tanh(x)))))) \\ _G. C. Greubel_, Jan 21 2018

%Y Cf. A009126.

%K sign,easy

%O 0,5

%A _R. H. Hardin_

%E Extended with signs by _Olivier GĂ©rard_, Mar 15 1997