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

Author

N. J. A. Sloane, May 29 2012

Keywords

• nonn
• tabf

Comments

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

Examples

			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 ...
  ...
		

Links

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

Crossrefs

Cf. A000108, A057545.

Formula

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

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