OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * 3^(n-k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * (-3)^(k-1) * a(n-k).
MATHEMATICA
nmax = 19; CoefficientList[Series[1/(1 - Log[1 + 3 x]/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! 3^(n - k), {k, 0, n}], {n, 0, 19}]
PROG
(PARI) my(x='x + O('x^20)); Vec(serlaplace(1/(1-log(1+3*x)/3))) \\ Michel Marcus, Jun 06 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 06 2022
STATUS
approved