%I #5 Feb 28 2022 08:11:03
%S 1,0,1,0,1,1,2,2,3,4,6,9,12,18,24,36,49,72,99,144,200,289,404,581,816,
%T 1168,1646,2350,3320,4730,6692,9522,13487,19174,27177,38614,54757,
%U 77771,110318,156646,222246,315526,447719,635569,901924,1280257,1816886,2578911
%N a(n) = (-1)^n + Sum_{k=0..floor((n-1)/2)} a(k) * a(n-2*k-1).
%F G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x^2))).
%t a[n_] := a[n] = (-1)^n + Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 47}]
%t nmax = 47; A[_] = 0; Do[A[x_] = 1/((1 + x) (1 - x A[x^2])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A000621, A005043, A351972.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Feb 26 2022