%I #9 Oct 20 2021 07:49:25

%S 1,4,28,295,4159,73348,1552468,38336569,1081926157,34350646636,

%T 1211796777748,47023762576987,1990643657768683,91291802205304972,

%U 4508735102829489580,238583762726054522989,13466532093135977880025,807606110028529741369396,51282242176105846536128236

%N a(n) = 1 + 3 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

%H Seiichi Manyama, <a href="/A343709/b343709.txt">Table of n, a(n) for n = 0..371</a>

%F E.g.f.: exp(x) / (1 + 3 * log(1 - x)).

%t a[n_] := a[n] = 1 + 3 Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]

%t nmax = 18; CoefficientList[Series[Exp[x]/(1 + 3 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

%o (PARI) N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+3*log(1-x)))) \\ _Seiichi Manyama_, Oct 20 2021

%Y Cf. A201354, A291979, A343707, A343710.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Apr 26 2021