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Expansion of e.g.f.: tanh(log(1+x))*log(1+x).
1

%I #17 Aug 26 2020 15:31:53

%S 0,0,2,-6,14,-20,-36,336,720,-38016,524160,-5448960,50388480,

%T -465903360,5010888960,-69353625600,1155961497600,-20593469030400,

%U 370356373094400,-6695551947571200,124010190839808000,-2408196729028608000

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

%F a(n) ~ (n-1)! * (-1)^n. - _Vaclav Kotesovec_, Jan 24 2015

%t CoefficientList[Series[(x*(2 + x)*Log[1 + x])/(2 + x*(2 + x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 24 2015 *)

%t With[{nn=30},CoefficientList[Series[Tanh[Log[1+x]]*Log[1+x],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 26 2020 *)

%K sign,easy

%O 0,3

%A _R. H. Hardin_

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

%E Definition clarified and first Mathematica program replaced by _Harvey P. Dale_, Aug 26 2020