%I #6 Apr 07 2019 00:00:23

%S 1,1,-1,-2,1,6,1,-18,-16,50,93,-112,-428,98,1713,936,-6004,-8382,

%T 17512,47608,-33826,-221936,-36335,892164,862666,-3051022,-6076072,

%U 8026380,32247334,-8222288,-144487267,-81500652,555489738,801700858,-1751543424,-4898513044

%N G.f. A(x) satisfies: A(x) = 1 + x - x^2*A(x)^2.

%F a(0) = a(1) = 1; a(n+2) = -Sum_{k=0..n} a(k)*a(n-k).

%e G.f.: A(x) = 1 + x - x^2 - 2*x^3 + x^4 + 6*x^5 + x^6 - 18*x^7 - 16*x^8 + 50*x^9 + 93*x^10 - 112*x^11 - 428*x^12 + ...

%t terms = 35; A[_] = 0; Do[A[x_] = 1 + x - x^2 A[x]^2 + O[x]^(terms + 1) // Normal, {terms + 1}]; CoefficientList[A[x], x]

%t a[0] = a[1] = 1; a[n_] := a[n] = -Sum[a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 35}]

%Y Cf. A007477, A104565.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, Apr 06 2019