A342770 T(n,k) is the number of rooted plane binary forests with n nodes and k trees: triangle read by rows.

1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 0, 3, 0, 1, 0, 1, 0, 5, 0, 3, 0, 1, 0, 1, 0, 0, 7, 0, 3, 0, 1, 0, 1, 0, 14, 0, 8, 0, 3, 0, 1, 0, 1, 0, 0, 22, 0, 8, 0, 3, 0, 1, 0, 1, 0, 42, 0, 24, 0, 8, 0, 3, 0, 1, 0, 1, 0, 0, 66, 0, 25, 0, 8, 0

Offset: 0

Author

R. J. Mathar, Mar 21 2021

Keywords

• nonn
• tabl

Comments

Multiset transform of A126120.

Examples

			See A222006 showing T(6,k).
The triangle starts (n>=0, 0<=k<=n):
  1
  0   1
  0   0   1
  0   1   0   1
  0   0   1   0   1
  0   2   0   1   0   1
  0   0   3   0   1   0   1
  0   5   0   3   0   1   0   1
  0   0   7   0   3   0   1   0   1
  0  14   0   8   0   3   0   1   0   1
  0   0  22   0   8   0   3   0   1   0   1
  0  42   0  24   0   8   0   3   0   1   0   1
  0   0  66   0  25   0   8   0   3   0   1   0   1
  0 132   0  74   0  25   0   8   0   3   0   1   0   1
  0   0 217   0  76   0  25   0   8   0   3   0   1   0   1
		

Crossrefs

Cf. A222006 (row sums), A126120 (column k=1), A007595 (k=2), A046342 (k=3), A088327 (limit n->oo, row reverse).