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%I #11 Feb 14 2022 03:53:42
%S 1,-15,235,-4200,86020,-2001055,52305780,-1520815230,48747603100,
%T -1709228504170,65115320810260,-2679459929923699,118482699493123571,
%U -5604477255138004835,282449438671531808676,-15111729578894643263239
%N Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1 + log(1+ x))))))^2 / 2.
%F a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000359(k) * A000359(n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+log(1+log(1+x)))))^2/2))
%o (PARI) T(n, k) = if(k==0, n==1, sum(j=0, n, abs(stirling(n, j, 1))*T(j, k-1)));
%o a(n) = (-1)^n*sum(k=1, n-1, binomial(n-1, k)*T(k, 5)*T(n-k, 5));
%Y Column 2 of A039817.
%Y Cf. A000359, A341587, A351515, A351525, A351526.
%K sign
%O 2,2
%A _Seiichi Manyama_, Feb 13 2022
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