cp's OEIS Frontend

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.

%I A385125 #11 Jun 22 2025 03:11:30
%S A385125 1,1,4,17,96,642,5238,50745,568976,7256750,103622742,1634819518,
%T A385125 28208152974,528060735100,10654676857578
%N 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.
%e A385125 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.
%e A385125   A:    __o__     B:    __o__
%e A385125        /  |  \         /  |  \
%e A385125      (1) (1) (2)     (3) (1) (2)
%e A385125      / \             / \
%e A385125    (1) (2)         (1) (2)
%o A385125 (PARI)
%o A385125 \\ See A385123 for Dx(N,B)
%o A385125 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]))}
%o A385125 Ax(5)
%Y A385125 Cf. Row sums of A385123.
%Y A385125 Cf. A000108, A107429, A384685, A384747.
%K A385125 nonn,more
%O A385125 0,3
%A A385125 _John Tyler Rascoe_, Jun 18 2025