A212808 Irregular triangle read by rows: row n gives number of cycles of length k in map on Catalan family of size n.

1, 1, 1, 1, 2, 0, 1, 5, 0, 1, 1, 14, 0, 1, 0, 0, 0, 2, 42, 0, 2, 3, 0, 1, 4, 132, 0, 2, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 429, 0, 2, 7, 0, 0, 28, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1

Offset

0,5

Comments

Length of n-th row: A057545(n)+1.

Links

Table of n, a(n) for n=0..74.

Robert Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.

Formula

T(n,0) = A000108(n).

T(n,0) = sum_{k>0} k*T(n,k) (see Donaghey, paragraph before (13)).

Example

Triangle begins
  1 1
  1 1
  2 0 1
  5 0 1 1
  14 0 1 0 0 0 2
  42 0 2 3 0 1 4
  132 0 2 0 0 0 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1
  429 0 2 7 0 0 28 0 0 1 1 0 0 0 0 1 0 0 0 0 2 0 0 0 1 ...
  ...

Crossrefs

Cf. A000108, A057545.

Sequence in context: A293961 A364228 A112899 * A337085 A209687 A108263

Adjacent sequences: A212805 A212806 A212807 * A212809 A212810 A212811

Keyword

nonn,tabf

Author

N. J. A. Sloane, May 29 2012

Status

approved