A372334 - OEIS

%I #16 Apr 30 2024 05:30:10

%S 0,1,8,102,2092,60140,2220954,100119670,5328468968,326960686872,

%T 22724388453070,1764411577328906,151364204180518476,

%U 14217940294767407380,1451334877597451677250,159972528561402504191190,18936257811933773637390544,2395818853376147403857700656

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

%H Seiichi Manyama, <a href="/A372334/b372334.txt">Table of n, a(n) for n = 0..334</a>

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

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

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

%F a(n) ~ exp(exp(-1)/3) * 3^(n-1) * n^(n-1). - _Vaclav Kotesovec_, Apr 30 2024

%o (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-exp(x)*lambertw(-3*x)/3)))

%o (PARI) a(n) = sum(k=1, n, (3*k)^(k-1)*binomial(n, k));

%Y Cf. A277473, A372333.

%Y Cf. A372316.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 28 2024