A394411 - OEIS

A394411

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 no two adjacent sibling nodes have the same weight.

1, 1, 2, 6, 17, 50, 155, 492, 1588, 5218, 17388, 58589, 199331, 683847, 2362995, 8216709, 28730796, 100958534, 356334303, 1262698652, 4490603094, 16022496932, 57339328443, 205761281668, 740232427023, 2669203547118, 9645606244577, 34925670593132, 126697320335584

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

FORMULA

G.f.: C(x) satisfies C(x) = 1/(1 - C(x) * Sum_{k>0} (x^k/(1 + x^k*C(x)))).

PROG

(PARI) C_x(N) = {my(x='x+O('x^(N+1)), A=1); for(i=1, N, A= 1/(1 - sum(k=1, N, x^k*A/(1 + x^k*A)))); Vec(A)}

CROSSREFS

Row sums of A393235.

Cf. A000108, A002212, A394284, A394385.