|
%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
|
