A351421 Expansion of e.g.f. -log(1 - log(1 + log(1+x))).

1, -1, 3, -13, 77, -576, 5219, -55567, 680028, -9405302, 145067040, -2468571128, 45936991110, -927915150852, 20219040931738, -472697857817078, 11801903989774760, -313395752536945568, 8819464678850030936, -262185434197432956664, 8210080944919085511680

Offset: 1

Author

Seiichi Manyama, Feb 11 2022

Keywords

• sign

Crossrefs

Column k=3 of A351420.

Cf. A000268, A130410.

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, 3]; Array[a, 21] (* Amiram Eldar, Feb 11 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(-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, 3);

Formula

a(n) = T(n,3), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.