%I #8 Mar 03 2022 04:34:32

%S 1,1,6,62,904,16984,390128,10586736,331267200,11738697600,

%T 464539452672,20302660659456,971106358760448,50452643588275200,

%U 2829000818124208128,170271405502300207104,10948525752699316371456,748994717201835804033024,54315931193865932254543872

%N Expansion of e.g.f. 1 / (1 + log(1 - 4*x) / 4).

%F a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * (-4)^(n-k).

%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * 4^(k-1) * a(n-k).

%F a(n) ~ n! * 4^(n+1) * exp(4*n) / (exp(4) - 1)^(n+1). - _Vaclav Kotesovec_, Mar 03 2022

%t nmax = 18; CoefficientList[Series[1/(1 + Log[1 - 4 x]/4), {x, 0, nmax}], x] Range[0, nmax]!

%t Table[Sum[StirlingS1[n, k] k! (-4)^(n - k), {k, 0, n}], {n, 0, 18}]

%o (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1+log(1-4*x)/4))) \\ _Michel Marcus_, Mar 02 2022

%Y Cf. A007840, A047053, A210246, A227917, A326324, A352069.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 02 2022