This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009566 #31 Jun 01 2024 12:06:48
%S A009566 0,1,-2,8,-47,359,-3349,36756,-462972,6574704,-103861896,1805930928,
%T A009566 -34267701720,704555489832,-15601914340440,370195510608192,
%U A009566 -9369769657984128,251979258929744448,-7175127496412091456
%N A009566 Expansion of e.g.f. sinh(log(1+log(1+x))).
%H A009566 G. C. Greubel, <a href="/A009566/b009566.txt">Table of n, a(n) for n = 0..415</a>
%F A009566 a(n) ~ n! * (-1)^(n+1) * exp(n) / (2 * (exp(1)-1)^(n+1)). - _Vaclav Kotesovec_, Jan 23 2015
%F A009566 a(n) = (-1)^(n-1)*((n-1)! + A007840(n))/2 for n > 0. - _Velin Yanev_, May 17 2024
%t A009566 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 A009566 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 A009566 (PARI) my(x='x+O('x^30)); concat([0], Vec(serlaplace(sinh(log(1+log(1+x)))))) \\ _G. C. Greubel_, Jan 21 2018
%K A009566 sign,easy
%O A009566 0,3
%A A009566 _R. H. Hardin_
%E A009566 Extended with signs by _Olivier Gérard_, Mar 15 1997