A362682 Expansion of e.g.f. exp(-LambertW(-x))/(1+x).

1, 0, 3, 7, 97, 811, 11941, 178557, 3354513, 69809383, 1659853861, 43658971753, 1268252733001, 40206626846283, 1383302292511413, 51308059650256741, 2041494097105707937, 86734131445797216847, 3919172491760452282693, 187679722656551406628833

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: -LambertW(-x)/(x * (1+x)).

a(n) = (-1)^n * n! * Sum_{k=0..n} (-(k+1))^k/(k+1)!.

a(0) = 1; a(n) = -n*a(n-1) + (n+1)^(n-1).

a(n) ~ exp(2) * n^(n-1) / (1 + exp(1)). - Vaclav Kotesovec, Aug 05 2025

E.g.f. A(x) satisfies A(x) = exp( x * (1+x) * A(x) ) / (1+x). - Seiichi Manyama, Oct 15 2025

Prog

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

Crossrefs

Cf. A102743, A277509.

Cf. A108919, A389782.

Sequence in context: A062592 A074349 A159310 * A299377 A129660 A373806

Adjacent sequences: A362679 A362680 A362681 * A362683 A362684 A362685

Keyword

nonn,easy

Author

Seiichi Manyama, May 01 2023

Status

approved