A351423 Expansion of e.g.f. -log(1 - log(1 + log(1 + log(1 + log(1+x))))).

1, -3, 16, -124, 1270, -16243, 249776, -4494334, 92716855, -2158505443, 55996266046, -1602132913687, 50124833578256, -1702501170925098, 62391472267252322, -2453892459756494459, 103101294099324376489, -4608723131704380915202

Offset: 1

Author

Seiichi Manyama, Feb 11 2022

Keywords

• sign

Crossrefs

Column k=5 of A351420.

Cf. A000359, A351428.

Programs

Mathematica

T[n_, 1] := (n - 1)!; T[n_, k_] := T[n, k] = Sum[StirlingS1[n, j] * T[j, k - 1], {j, 1, n}]; a[n_] := T[n, 5]; Array[a, 18] (* Amiram Eldar, Feb 11 2022 *)

PARI

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

PARI

T(n, k) = if(k==1, (n-1)!, sum(j=1, n, stirling(n, j, 1)*T(j, k-1)));
a(n) = T(n, 5);

Formula

a(n) = T(n,5), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.