A368445 Expansion of e.g.f. exp(x) / (1 + log(1 - 3*x)).

1, 4, 34, 469, 8815, 208348, 5922118, 196568419, 7459854973, 318560689324, 15116763184978, 789119869380577, 44939583072146251, 2772582488089509028, 184216538154508055062, 13114092114632287359919, 995813104288130697683065, 80342826520464644566291828

Offset: 0

Author

Seiichi Manyama, Dec 24 2023

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..357

Crossrefs

Cf. A291979, A368444.

Cf. A343709.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[x]/(1+Log[1-3x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 07 2025 *)

PARI

a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 3^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Formula

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