A034799 Triangle read by rows: T(n,k) is the number of partially labeled trees with n nodes, k of which are labeled, 0 <= k <= n.

1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 4, 9, 16, 16, 3, 9, 26, 67, 125, 125, 6, 20, 75, 251, 680, 1296, 1296, 11, 48, 214, 888, 3135, 8716, 16807, 16807, 23, 115, 612, 3023, 13155, 47787, 134960, 262144, 262144, 47, 286, 1747, 10038, 51873, 232154, 858578, 2450309, 4782969, 4782969

Offset

0,8

References

J. Riordan, An Introduction to Combinatorial Analysis, p. 138.

Links

Table of n, a(n) for n=0..54.

Index entries for sequences related to trees

Formula

Reference gives generating function.

E.g.f.: r(x,y) - (1/2)*r(x,y)^2 + (1/2)*r(x^2) where r(x,y) is the e.g.f. for A008295 and r(x) is the o.g.f. for A000081. - Sean A. Irvine, Sep 04 2020

Example

Triangle begins:
  1;
  1, 1;
  1, 1, 1;
  1, 2, 3, 3;
  2, 4, 9, 16, 16;
  ...

Crossrefs

Columns are A000055, A000081, A000243, A000269, A000485, A000526, A064785.

Cf. A008295, A034800.

Sequence in context: A343326 A073078 A360296 * A008985 A326699 A138652

Adjacent sequences: A034796 A034797 A034798 * A034800 A034801 A034802

Keyword

nonn,tabl

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Sep 04 2020

Name edited by Andrew Howroyd, Mar 23 2023

Status

approved