A396746 - OEIS

%I #10 Jun 04 2026 09:35:42

%S 1,4,33,420,7305,162198,4398933,141259912,5248415169,221637262410,

%T 10489037239989,549976658760972,31650208550358801,1983383546128436494,

%U 134440159552418677365,9800566084124471843472,764564284108064457174273,63552209174719502953891986

%N Expansion of e.g.f. -W_3(-x)/(1 - W_3(-x)), where W_k(x) is the k-th iterate of LambertW(x).

%F E.g.f.: 1 - exp(-B(x)), where B(x) is the e.g.f. of A396678.

%F a(n) = Sum_{k=1..n} n^(n-k) * binomial(n-1,k-1) * A396745(k).

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

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

%Y Column k=3 of A396744.

%Y Cf. A396678, A396713, A396745.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jun 04 2026