The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #8 Oct 20 2021 07:49:21
%S 1,5,45,609,11009,248837,6749629,213596401,7725031521,314310704101,
%T 14209394894765,706617979262049,38333841625642785,2252901018519028901,
%U 142589176837851349757,9669282207517755852721,699408060608904410296897,53752166013267632536864581,4374061543586452325644329133
%N a(n) = 1 + 4 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).
%H Seiichi Manyama, <a href="/A343710/b343710.txt">Table of n, a(n) for n = 0..359</a>
%F E.g.f.: exp(x) / (1 + 4 * log(1 - x)).
%t a[n_] := a[n] = 1 + 4 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 + 4 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+4*log(1-x)))) \\ _Seiichi Manyama_, Oct 20 2021
%Y Cf. A201365, A291979, A343707, A343709.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 26 2021