A368177 - OEIS

%I #14 Mar 11 2024 05:05:54

%S 0,1,7,47,402,4569,65298,1119789,22397112,511972065,13166163630,

%T 376208954109,11824734538620,405454640476833,15061050695642994,

%U 602494304797738845,25823425094211472272,1180601869774944168513,57348495330075309426390

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

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

%F a(n) ~ (n-1)! * 3^n / LambertW(3)^n. - _Vaclav Kotesovec_, Mar 11 2024

%t With[{nn=20},CoefficientList[Series[-Log[1-x Exp[3x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 10 2024 *)

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

%Y Cf. A009306, A009444, A368176.

%Y Cf. A336951.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Dec 14 2023