cp's OEIS Frontend

A384748 Number of rooted ordered trees with node weights summing to n, where the root has weight 0, non-root node weights are greater than 0, and no nodes have the same weight as their parent node.

%I A384748 #15 Jun 12 2025 00:49:50
%S A384748 1,1,2,6,16,44,128,376,1114,3346,10152,31028,95474,295532,919446,
%T A384748 2873388,9015812,28390466,89689586,284173096,902780060,2875016084,
%U A384748 9176388532,29349499212,94050228650,301918397716,970815092346
%N A384748 Number of rooted ordered trees with node weights summing to n, where the root has weight 0, non-root node weights are greater than 0, and no nodes have the same weight as their parent node.
%e A384748 a(3) = 6 counts:
%e A384748   o    o    o      o        o        __o__
%e A384748   |    |    |     / \      / \      /  |  \
%e A384748  (3)  (2)  (1)  (1) (2)  (2) (1)  (1) (1) (1)
%e A384748        |    |
%e A384748       (1)  (2)
%o A384748 (PARI)
%o A384748 b(i,j,k,N) = {if(k>N,1, 1/(1-sum(u=1,j, if(u==i,0,x^u*b(u,j,k+1,N-u+1)))))}
%o A384748 Dx(N) = {my(x='x+O('x^(N+1))); Vec(1/(1 - sum(i=1,N, b(i,N,1,N)*x^i)))}
%o A384748 Dx(10)
%Y A384748 Cf. A000108, A002212, A143330, A384613, A384685, (main diagonal of A384747).
%K A384748 nonn,more
%O A384748 0,3
%A A384748 _John Tyler Rascoe_, Jun 09 2025
%E A384748 a(14)-a(26) from _David Radcliffe_, Jun 10 2025