A394285 Number of ordered rooted trees with node weights summing to n; such that the root has weight 0, non-root nodes have positive integer weights, and only nodes of even weight can have branches.

1, 1, 2, 5, 12, 31, 81, 218, 596, 1656, 4658, 13244, 37999, 109885, 319943, 937164, 2759739, 8165427, 24262526, 72369917, 216615341, 650420722, 1958645383, 5913849653, 17899739496, 54300572393, 165071280286, 502786720049, 1534205598328, 4689416829159, 14356303196762

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

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

Prog

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

Crossrefs

Row sums of A394284.

Cf. A000108, A107131, A384748.

Sequence in context: A110035 A000635 A317098 * A238427 A077556 A076906

Adjacent sequences: A394282 A394283 A394284 * A394286 A394287 A394288

Keyword

nonn,easy

Author

John Tyler Rascoe, Mar 14 2026

Status

approved