A351527 Expansion of e.g.f. (log(1 + log(1 + log(1 + log(1 + log(1+ x))))))^2 / 2.

1, -15, 235, -4200, 86020, -2001055, 52305780, -1520815230, 48747603100, -1709228504170, 65115320810260, -2679459929923699, 118482699493123571, -5604477255138004835, 282449438671531808676, -15111729578894643263239

Offset: 2

Author

Seiichi Manyama, Feb 13 2022

Keywords

• sign

Crossrefs

Column 2 of A039817.

Cf. A000359, A341587, A351515, A351525, A351526.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(log(1+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, 5)*T(n-k, 5));

Formula

a(n) = (-1)^n * Sum_{k=1..n-1} binomial(n-1,k) * A000359(k) * A000359(n-k).