A394406 - OEIS

%I #4 Mar 23 2026 22:18:17

%S 1,1,3,9,30,105,384,1449,5604,22098,88518,359199,1473510,6100674,

%T 25459458,106983387,452284206,1922339874,8209529058,35209578564,

%U 151591511244,654942504858,2838635631636,12338881238403,53777141269638,234954571294164,1028852856643566

%N Number of ordered rooted trees with non-root node weights summing to n such that the root has weight 0, non-root nodes have positive integer weights, and only non-root nodes of odd weight can have branches.

%F G.f.: (1 - 2*x^2 - (1 - x^2)*sqrt((1 - x^2/(1 - x^2))^2 - 4*x/(1 - x^2)))/(2*x).

%o (PARI) C_x(N) = {my(x='x+O('x^(N+1))); Vec((1 - 2*x^2 - (1 - x^2)*sqrt((1 - x^2/(1 - x^2))^2 - 4*x/(1 - x^2)))/(2*x))}

%Y Cf. Row sums of A394386.

%Y Cf. A000108, A002212, A394285.

%K nonn,easy

%O 0,3

%A _John Tyler Rascoe_, Mar 19 2026