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%I #9 Mar 26 2019 11:53:27
%S 0,1,2,4,0,-104,-1200,-10352,-68992,-177536,5310720,145374208,
%T 2512029696,33484862464,294806779904,-1053894275072,-133585065738240,
%U -4148745576218624,-92116699894185984,-1510783598900412416,-11327731683300474880,414155615537321476096,25541948643911385219072
%N Expansion of e.g.f. tanh(x/(1 - x)).
%C Lah transform of the sequence 0, 1, 0, -2, 0, 16, 0, -272, ... (A155585 with initial term 0).
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p a:=series(tanh(x/(1 - x)), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # _Paolo P. Lava_, Mar 26 2019
%t nmax = 22; CoefficientList[Series[Tanh[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[Binomial[n - 1, k - 1] 2^k EulerE[k, 1] n!/k!, {k, n}], {n, 0, 22}]
%Y Cf. A000182, A155585, A219613.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Jul 27 2018
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