A351526 Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1+ x)))))^2 / 2.

1, -12, 152, -2210, 36976, -704837, 15132932, -362099010, 9566898126, -276863733707, 8715530417502, -296641340905299, 10858928017129838, -425542158316462627, 17779220784851800828, -789053832262002586555, 37076561046965367191298

Offset: 2

Author

Seiichi Manyama, Feb 13 2022

Keywords

• sign

Crossrefs

Column 2 of A039816.

Cf. A000310, A341587, A351514, A351525, A351527.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+log(1+log(1+log(1+x))))^2/2))

PARI

T(n, k) = if(k==0, n==1, sum(j=0, n, abs(stirling(n, j, 1))*T(j, k-1)));
a(n) = (-1)^n*sum(k=1, n-1, binomial(n-1, k)*T(k, 4)*T(n-k, 4));

Formula

a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000310(k) * A000310(n-k).