A396677 Expansion of e.g.f. log(1 - W_2(-x)), where W_k(x) is the k-th iterate of LambertW(x).

1, 3, 20, 206, 2884, 51222, 1104970, 28092136, 823228920, 27337210010, 1014889977694, 41663456547924, 1874254936175764, 91693069544415094, 4846976442380146890, 275307423965422835888, 16721766342325378632688, 1081506161649434021320626, 74206134445040935320645046

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = Sum_{k=1..n} n^(n-k) * binomial(n-1,k-1) * A133297(k).

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

Prog

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

Crossrefs

Column k=2 of A396675.

Cf. A133297, A207833.

Sequence in context: A052590 A081209 A196560 * A257476 A218673 A230478

Adjacent sequences: A396674 A396675 A396676 * A396678 A396679 A396680

Keyword

nonn

Author

Seiichi Manyama, Jun 02 2026

Status

approved