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

0,3

Links

Table of n, a(n) for n=0..18.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A009306, A009444, A368176.

Cf. A336951.

Sequence in context: A108434 A349255 A093173 * A218761 A173772 A178002

Adjacent sequences: A368174 A368175 A368176 * A368178 A368179 A368180

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 14 2023

Status

approved