A396679 Expansion of e.g.f. -log(1 + W_2(-x)), where W_k(x) is the k-th iterate of LambertW(x).

1, 5, 44, 554, 9084, 183702, 4421038, 123461928, 3925948968, 140087469050, 5543906536794, 241013315412036, 11418689731291036, 585622428410061798, 32325218349324188670, 1910820256385689252208, 120436526080379248980816, 8062820108466517571361138

Offset

1,2

Links

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

Formula

a(n) = Sum_{k=1..n} n^(n-k) * binomial(n-1,k-1) * A001865(k).

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

a(n) ~ sqrt(Pi/2) * exp(exp(-1)*n) * n^(n - 1/2) * (1 - sqrt(2/((1 - exp(-1)) * Pi*n))/3). - Vaclav Kotesovec, Jun 29 2026

Prog

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

Crossrefs

Column k=2 of A396676.

Cf. A001865, A207833.

Sequence in context: A215648 A195242 A243697 * A106273 A349836 A052803

Adjacent sequences: A396676 A396677 A396678 * A396680 A396682 A396683

Keyword

nonn

Author

Seiichi Manyama, Jun 02 2026

Status

approved