A362860 - OEIS

%I #12 May 06 2023 09:00:52

%S 1,2,31,629,18025,662639,29752957,1578248867,96577834801,

%T 6696994946543,518978239136341,44448540938239811,4169223860364566857,

%U 425060509005908328071,46801425208023247277965,5534686715620432932442619,699654866766940182167273185

%N Expansion of e.g.f. exp(-x) / (1 + LambertW(-3*x)).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F G.f.: Sum_{k>=0} (3*k*x)^k / (1 + x)^(k+1).

%F a(n) = (-1)^n * Sum_{k=0..n} (-3*k)^k * binomial(n,k).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-x)/(1 + lambertw(-3*x))))

%Y Column k=3 of A362019.

%Y Cf. A091482, A362858.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, May 05 2023