%I #7 Aug 14 2021 04:21:19
%S 1,0,0,-1,-1,-1,0,4,15,40,86,134,16,-1060,-6119,-25187,-86678,-250846,
%T -537819,-175233,6998009,55632942,310923272,1465146781,6011047682,
%U 20719304348,49356093300,-36579100806,-1549214884054,-13807417413199,-92912464763743
%N G.f. A(x) satisfies: A(x) = 1 - x^3 * A(x/(1 - x)) / (1 - x).
%H Seiichi Manyama, <a href="/A336971/b336971.txt">Table of n, a(n) for n = 0..704</a>
%F a(0) = 1, a(1) = a(2) = 0; a(n) = -Sum_{k=0..n-3} binomial(n-3,k) * a(k).
%t nmax = 30; A[_] = 0; Do[A[x_] = 1 - x^3 A[x/(1 - x)]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 30}]
%Y Cf. A000587, A000996, A336970.
%K sign
%O 0,8
%A _Ilya Gutkovskiy_, Aug 09 2020