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A331339 E.g.f.: 1 / (1 + log(1 - x - x^2)).

%I A331339 #8 Aug 20 2021 05:44:19
%S A331339 1,1,5,32,292,3294,44918,714468,13002456,266275200,6060498672,
%T A331339 151750887936,4145522908272,122690391196944,3910569680464848,
%U A331339 133549150323123744,4864927063250290176,188297220693251438208,7716800776602560577408
%N A331339 E.g.f.: 1 / (1 + log(1 - x - x^2)).
%F A331339 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k - 1)! * Lucas(k) * a(n-k).
%F A331339 a(n) ~ n! * 2^(n+1) * exp(n/2) / (sqrt(5*exp(1) - 4) * (sqrt(5*exp(1) - 4) - exp(1/2))^(n+1)). - _Vaclav Kotesovec_, Jan 26 2020
%p A331339 A331339 := proc(n)
%p A331339     option remember;
%p A331339     if n = 0 then
%p A331339         1;
%p A331339     else
%p A331339         add(binomial(n,k)*(k-1)!*A000204(k)*procname(n-k),k=1..n) ;
%p A331339     end if;
%p A331339 end proc:
%p A331339 seq(A331339(n),n=0..42) ; # _R. J. Mathar_, Aug 20 2021
%t A331339 nmax = 18; CoefficientList[Series[1/(1 + Log[1 - x - x^2]), {x, 0, nmax}], x] Range[0, nmax]!
%t A331339 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! LucasL[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
%Y A331339 Cf. A000204, A007840, A039647.
%K A331339 nonn
%O A331339 0,3
%A A331339 _Ilya Gutkovskiy_, Jan 14 2020