%I #8 Aug 14 2021 04:20:58
%S 1,0,-1,-1,0,3,9,16,7,-87,-472,-1567,-3375,-216,45927,308107,1372744,
%T 4351599,5711849,-49345432,-547773585,-3517370859,-16914970464,
%U -56474505155,-25470754271,1593389360016,17323737305039,125785962635543,706598399399184
%N G.f. A(x) satisfies: A(x) = 1 - x^2 * A(x/(1 - x)) / (1 - x).
%H Seiichi Manyama, <a href="/A336970/b336970.txt">Table of n, a(n) for n = 0..657</a>
%F a(0) = 1, a(1) = 0; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k).
%t nmax = 28; A[_] = 0; Do[A[x_] = 1 - x^2 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 - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 28}]
%Y Cf. A000587, A000994, A336971.
%K sign
%O 0,6
%A _Ilya Gutkovskiy_, Aug 09 2020