A212808 - OEIS

%I #18 Jan 11 2024 03:02:20

%S 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,

%T 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,

%U 1,0,0,0,0,2,0,0,0,1

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

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

%H Robert Donaghey, <a href="https://doi.org/10.1016/0095-8956(80)90045-3">Automorphisms on Catalan trees and bracketing</a>, J. Combin. Theory, Series B, 29 (1980), 75-90.

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

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

%e Triangle begins

%e   1 1

%e   1 1

%e   2 0 1

%e   5 0 1 1

%e   14 0 1 0 0 0 2

%e   42 0 2 3 0 1 4

%e   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

%e   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 ...

%e   ...

%Y Cf. A000108, A057545.

%K nonn,tabf

%O 0,5

%A _N. J. A. Sloane_, May 29 2012