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.

1, 1, 2, 6, 16, 44, 128, 376, 1114, 3346, 10152, 31028, 95474, 295532, 919446, 2873388, 9015812, 28390466, 89689586, 284173096, 902780060, 2875016084, 9176388532, 29349499212, 94050228650, 301918397716, 970815092346

Offset: 0

Author

John Tyler Rascoe, Jun 09 2025

Keywords

• nonn
• more

Examples

			a(3) = 6 counts:
  o    o    o      o        o        __o__
  |    |    |     / \      / \      /  |  \
 (3)  (2)  (1)  (1) (2)  (2) (1)  (1) (1) (1)
       |    |
      (1)  (2)
		

Crossrefs

Cf. A000108, A002212, A143330, A384613, A384685, (main diagonal of A384747).

Programs

PARI

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)))))}
Dx(N) = {my(x='x+O('x^(N+1))); Vec(1/(1 - sum(i=1,N, b(i,N,1,N)*x^i)))}
Dx(10)

Extensions

a(14)-a(26) from David Radcliffe, Jun 10 2025