OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * 4^(n-k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * (-4)^(k-1) * a(n-k).
MATHEMATICA
nmax = 18; CoefficientList[Series[1/(1 - Log[1 + 4 x]/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! 4^(n - k), {k, 0, n}], {n, 0, 18}]
PROG
(PARI) my(x='x + O('x^20)); Vec(serlaplace(1/(1-log(1+4*x)/4))) \\ Michel Marcus, Jun 06 2022
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 06 2022
STATUS
approved