A385125 Number of rooted ordered trees with n non-root nodes all labeled with numbers greater than 0 such that the labels of all groups of sibling nodes cover the same initial interval.

1, 1, 4, 17, 96, 642, 5238, 50745, 568976, 7256750, 103622742, 1634819518, 28208152974, 528060735100, 10654676857578

Offset: 0

Author

John Tyler Rascoe, Jun 18 2025

Keywords

• nonn
• more

Examples

			Tree A has sibling node groups whose labels both cover the initial interval (1,2). Tree B has sibling node groups whose labels cover the initial intervals (1,2) and (1,2,3). So tree A is counted under a(5) = 642 while tree B is not.
  A:    __o__     B:    __o__
       /  |  \         /  |  \
     (1) (1) (2)     (3) (1) (2)
     / \             / \
   (1) (2)         (1) (2)
		

Crossrefs

Cf. Row sums of A385123.

Cf. A000108, A107429, A384685, A384747.

Programs

PARI

\\ See A385123 for Dx(N,B)
Ax(N) = {my( v = vector(N, i, if(i==1, 1, 0))~); for(k=1, N, v=matconcat([v, Dx(N+1, vector(k,i,i))~])); vector(N, n, sum(i=1, n, v[n, i]))}
Ax(5)