A396746 Expansion of e.g.f. -W_3(-x)/(1 - W_3(-x)), where W_k(x) is the k-th iterate of LambertW(x).

1, 4, 33, 420, 7305, 162198, 4398933, 141259912, 5248415169, 221637262410, 10489037239989, 549976658760972, 31650208550358801, 1983383546128436494, 134440159552418677365, 9800566084124471843472, 764564284108064457174273, 63552209174719502953891986

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

E.g.f.: 1 - exp(-B(x)), where B(x) is the e.g.f. of A396678.

a(n) = Sum_{k=1..n} n^(n-k) * binomial(n-1,k-1) * A396745(k).

a(n) = (n-1)! * Sum_{i,j,k,l >= 0 and i+j+k+l=n-1} (-1)^l * (l+1) * n^i * (n-i)^j * (n-i-j)^k / (i!*j!*k!).

Prog

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

Crossrefs

Column k=3 of A396744.

Cf. A396678, A396713, A396745.

Sequence in context: A360234 A111534 A162655 * A216135 A052885 A277184

Adjacent sequences: A396743 A396744 A396745 * A396749 A396750 A396751

Keyword

nonn

Author

Seiichi Manyama, Jun 04 2026

Status

approved