A009444 -id:A009444 - cp's OEIS frontend

A368176 Expansion of e.g.f. -log(1 - x * exp(2*x)).

0, 1, 5, 26, 182, 1704, 19992, 281392, 4620464, 86707584, 1830550400, 42940149504, 1107995749632, 31188982438912, 951100528802816, 31234626965637120, 1099029746752575488, 41248797730190032896, 1644909773059509682176

Offset: 0

Seiichi Manyama, Dec 14 2023

Cf. A009306, A009444, A368177.

Cf. A336950.

a(n) = sum(k=1, n, (2*k)^(n-k)*(k-1)!*binomial(n, k));

a(n) = Sum_{k=1..n} (2*k)^(n-k) * (k-1)! * binomial(n,k).

a(n) ~ (n-1)! * 2^n / LambertW(2)^n. - Vaclav Kotesovec, Mar 11 2024

A368177 Expansion of e.g.f. -log(1 - x * exp(3*x)).

Original entry on oeis.org

0, 1, 7, 47, 402, 4569, 65298, 1119789, 22397112, 511972065, 13166163630, 376208954109, 11824734538620, 405454640476833, 15061050695642994, 602494304797738845, 25823425094211472272, 1180601869774944168513, 57348495330075309426390

Offset: 0

Seiichi Manyama, Dec 14 2023

Cf. A009306, A009444, A368176.

Cf. A336951.

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

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

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

cp's OEIS Frontend

A368176 Expansion of e.g.f. -log(1 - x * exp(2*x)).

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