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

0,17

Comments

Multiset transform of A126120.

Links

Table of n, a(n) for n=0..85.

Example

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).

Sequence in context: A065717 A070092 A365545 * A341519 A307837 A123671

Adjacent sequences: A342767 A342768 A342769 * A342771 A342772 A342773

Keyword

nonn,tabl

Author

R. J. Mathar, Mar 21 2021

Status

approved