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%I #5 Feb 18 2022 03:04:34
%S 1,-1,-1,2,10,10,-97,-638,-1316,9908,118713,560533,-697429,-38229322,
%T -364288567,-1441996161,11586777849,281338444108,2772828770441,
%U 10249821640498,-170439385810217,-4104012197171264,-46232949019802137,-204897893603728741,3708422726478663919
%N G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)^2) / (1 - x)^2.
%F a(0) = 1; a(n) = -Sum_{k=0..n-1} binomial(n+k,n-k-1) * a(k).
%t nmax = 24; A[_] = 0; Do[A[x_] = 1 - x A[x/(1 - x)^2]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n + k, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 24}]
%Y Cf. A000587, A014619, A125274, A351658.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Feb 16 2022