A394406 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.

1, 1, 3, 9, 30, 105, 384, 1449, 5604, 22098, 88518, 359199, 1473510, 6100674, 25459458, 106983387, 452284206, 1922339874, 8209529058, 35209578564, 151591511244, 654942504858, 2838635631636, 12338881238403, 53777141269638, 234954571294164, 1028852856643566

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

Prog

(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))}

Crossrefs

Cf. Row sums of A394386.

Cf. A000108, A002212, A394285.

Sequence in context: A003409 A029651 A316371 * A181933 A148957 A148958

Adjacent sequences: A394403 A394404 A394405 * A394407 A394408 A394409

Keyword

nonn,easy

Author

John Tyler Rascoe, Mar 19 2026

Status

approved