A396677 - OEIS

%I #13 Jun 02 2026 11:47:54

%S 1,3,20,206,2884,51222,1104970,28092136,823228920,27337210010,

%T 1014889977694,41663456547924,1874254936175764,91693069544415094,

%U 4846976442380146890,275307423965422835888,16721766342325378632688,1081506161649434021320626,74206134445040935320645046

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

%F a(n) = Sum_{k=1..n} n^(n-k) * binomial(n-1,k-1) * A133297(k).

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

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

%Y Column k=2 of A396675.

%Y Cf. A133297, A207833.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 02 2026