A396557 Expansion of e.g.f. -LambertW(-LambertW(-LambertW(-x))).

0, 1, 2, 15, 124, 1605, 23826, 446131, 9494696, 234924633, 6489737830, 200530623711, 6804957067404, 252717429733093, 10170665548897322, 441656425701309435, 20567515843800970576, 1023126772183618699185, 54132939273244418609742, 3036227079039027495953815

Offset

0,3

Links

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

Formula

a(n) ~ sqrt(LambertW(-LambertW(-exp(-1+exp(-1)-exp(-1+exp(-1)))))) * n^(n-1) * exp(1/2 - n*exp(-1) + n*exp(-1+exp(-1))) / (sqrt(1+LambertW(-LambertW(-exp(-1+exp(-1)-exp(-1+exp(-1)))))) * sqrt(1+LambertW(-exp(-1+exp(-1)-exp(-1+exp(-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, A227278, A207833, A340474, A396556, A396558.

Sequence in context: A341726 A055866 A364978 * A051407 A371580 A390743

Adjacent sequences: A396554 A396555 A396556 * A396558 A396559 A396560

Keyword

nonn

Author

Vaclav Kotesovec, May 29 2026

Status

approved