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%I #31 Jun 01 2024 12:06:48
%S 0,1,-2,8,-47,359,-3349,36756,-462972,6574704,-103861896,1805930928,
%T -34267701720,704555489832,-15601914340440,370195510608192,
%U -9369769657984128,251979258929744448,-7175127496412091456
%N Expansion of e.g.f. sinh(log(1+log(1+x))).
%H G. C. Greubel, <a href="/A009566/b009566.txt">Table of n, a(n) for n = 0..415</a>
%F a(n) ~ n! * (-1)^(n+1) * exp(n) / (2 * (exp(1)-1)^(n+1)). - _Vaclav Kotesovec_, Jan 23 2015
%F a(n) = (-1)^(n-1)*((n-1)! + A007840(n))/2 for n > 0. - _Velin Yanev_, May 17 2024
%t CoefficientList[Series[(Log[1 + x]*(2 + Log[1 + x]))/(2*(1 + Log[1 + x]) ), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jan 23 2015 *)
%t With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + Log[1 + x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jan 21 2018 *)
%o (PARI) my(x='x+O('x^30)); concat([0], Vec(serlaplace(sinh(log(1+log(1+x)))))) \\ _G. C. Greubel_, Jan 21 2018
%K sign,easy
%O 0,3
%A _R. H. Hardin_
%E Extended with signs by _Olivier Gérard_, Mar 15 1997