A396558 Expansion of e.g.f. LambertW(-LambertW(LambertW(-x))).

0, 1, 2, 15, 148, 2085, 36846, 794731, 20193048, 591807033, 19656536410, 729997181991, 29979371909268, 1349164389219829, 66029153271279030, 3491587496153702835, 198385745127056113456, 12053203457258475087729, 779766900035700212338482, 53515498602863186777511487

Offset

0,3

Links

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

Formula

a(n) ~ n^(n-1) * exp(n*exp(-1)) * LambertW(1) / (sqrt(1-exp(-1)) * (1 + LambertW(1))).

a(n) = Sum_{i,j,k >= 0 and i+j+k=n-1} ((n-1)!/(i!*j!*k!)) * n^i * (n-i)^j * (-(k+1))^k. - Seiichi Manyama, May 31 2026

Mathematica

nmax = 20; CoefficientList[Series[LambertW[-LambertW[LambertW[-x]]], {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A097174, A227176, A227278, A207833, A396556, A396557.

Sequence in context: A371582 A001854 A060226 * A325060 A002103 A191364

Adjacent sequences: A396555 A396556 A396557 * A396559 A396560 A396561

Keyword

nonn

Author

Vaclav Kotesovec, May 29 2026

Status

approved