A396745 Expansion of e.g.f. -W_2(-x)/(1 - W_2(-x)), where W_k(x) is the k-th iterate of LambertW(x).

1, 2, 12, 116, 1560, 26982, 571816, 14364744, 417579840, 13792134410, 510196667904, 20895180920748, 938534383139392, 45870090395524878, 2423239548338828160, 137588517622985053328, 8355165072715731427584, 540325701493027420663314, 37072240616242863767710720

Offset

1,2

Links

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

Formula

E.g.f.: 1 - exp(-B(x)), where B(x) is the e.g.f. of A396677.

a(n) = Sum_{k=1..n} n^(n-k) * binomial(n-1,k-1) * A277458(k).

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

Prog

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

Crossrefs

Column k=2 of A396744.

Cf. A277458, A396677, A396712.

Sequence in context: A035051 A214222 A227459 * A377716 A380425 A372200

Adjacent sequences: A396742 A396743 A396744 * A396746 A396749 A396750

Keyword

nonn

Author

Seiichi Manyama, Jun 04 2026

Status

approved