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%I #12 Feb 14 2022 03:53:26
%S 1,-12,152,-2210,36976,-704837,15132932,-362099010,9566898126,
%T -276863733707,8715530417502,-296641340905299,10858928017129838,
%U -425542158316462627,17779220784851800828,-789053832262002586555,37076561046965367191298
%N Expansion of e.g.f. (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) * A000310(k) * A000310(n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(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, 4)*T(n-k, 4));
%Y Column 2 of A039816.
%Y Cf. A000310, A341587, A351514, A351525, A351527.
%K sign
%O 2,2
%A _Seiichi Manyama_, Feb 13 2022
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