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%I #5 Feb 08 2022 05:19:22
%S 0,0,1,0,0,1,-3,6,-9,6,27,-169,645,-1995,5122,-9570,1242,109739,
%T -756648,3733128,-15527337,55626585,-161247102,260402511,1028417064,
%U -14243992155,102551438561,-595149283191,3010031905815,-13336771020834,48891499316016,-111677138548476
%N G.f. A(x) satisfies: A(x) = x^2 + x^3 * A(x/(1 + x)) / (1 + x).
%C Shifts 3 places left under inverse binomial transform.
%F a(0) = a(1) = 0, a(2) = 1; a(n) = Sum_{k=0..n-3} (-1)^k * binomial(n-3,k) * a(n-k-3).
%t nmax = 31; A[_] = 0; Do[A[x_] = x^2 + x^3 A[x/(1 + x)]/(1 + x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = a[1] = 0; a[2] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n - 3, k] a[n - k - 3], {k, 0, n - 3}]; Table[a[n], {n, 0, 31}]
%Y Cf. A000998, A010741, A351188.
%K sign
%O 0,7
%A _Ilya Gutkovskiy_, Feb 04 2022