A394239 Expansion of e.g.f. exp(-LambertW(LambertW(-LambertW(x)))).

1, 1, 3, 22, 185, 2396, 33577, 627586, 12425793, 304670440, 7834984721, 238210064654, 7556171275633, 274457126457580, 10369007661180729, 438234736977732706, 19226494214723368193, 927145432220682846800, 46342321326549429922081, 2511493881689133031922326

Offset

0,3

Links

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

Formula

E.g.f.: exp(B(x)), where B(x) is the e.g.f. of A396556.

a(0) = 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+2)^k.

a(n) ~ exp(1+n*exp(-1)-n*exp(-1-exp(-1))) * n^(n-1) / (sqrt(1-exp(-1)) * sqrt(1+exp(-1-exp(-1)))). - Vaclav Kotesovec, Jun 01 2026

Prog

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

Crossrefs

Cf. A268653, A340474, A395376.

Cf. A396556.

Sequence in context: A387036 A354327 A278333 * A132595 A065204 A001393

Adjacent sequences: A394236 A394237 A394238 * A394240 A394241 A394242

Keyword

nonn

Author

Seiichi Manyama, Jun 01 2026

Status

approved