A368177 Expansion of e.g.f. -log(1 - x * exp(3*x)).
0, 1, 7, 47, 402, 4569, 65298, 1119789, 22397112, 511972065, 13166163630, 376208954109, 11824734538620, 405454640476833, 15061050695642994, 602494304797738845, 25823425094211472272, 1180601869774944168513, 57348495330075309426390
Offset: 0
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[-Log[1-x Exp[3x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 10 2024 *) -
PARI
a(n) = sum(k=1, n, (3*k)^(n-k)*(k-1)!*binomial(n, k));
Formula
a(n) = Sum_{k=1..n} (3*k)^(n-k) * (k-1)! * binomial(n,k).
a(n) ~ (n-1)! * 3^n / LambertW(3)^n. - Vaclav Kotesovec, Mar 11 2024