A351526 - OEIS

%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