A351422 Expansion of e.g.f. -log(1 - log(1 + log(1 + log(1+x)))).

1, -2, 8, -48, 386, -3905, 47701, -683592, 11250291, -209168071, 4336482905, -99197868847, 2481962140797, -67426166949102, 1976463051528507, -62178381389729317, 2089532143617395264, -74702625442877063902, 2830904065389397804534, -113348477836878447492630

Offset: 1

Author

Seiichi Manyama, Feb 11 2022

Keywords

• sign

Crossrefs

Column k=4 of A351420.

Cf. A000310, A351427.

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, 4]; Array[a, 20] (* Amiram Eldar, Feb 11 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(-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, 4);

Formula

a(n) = T(n,4), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.