cp's OEIS Frontend

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

%I A212808 #18 Jan 11 2024 03:02:20
%S A212808 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 A212808 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 A212808 1,0,0,0,0,2,0,0,0,1
%N A212808 Irregular triangle read by rows: row n gives number of cycles of length k in map on Catalan family of size n.
%C A212808 Length of n-th row: A057545(n)+1.
%H A212808 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 A212808 T(n,0) = A000108(n).
%F A212808 T(n,0) = sum_{k>0} k*T(n,k) (see Donaghey, paragraph before (13)).
%e A212808 Triangle begins
%e A212808   1 1
%e A212808   1 1
%e A212808   2 0 1
%e A212808   5 0 1 1
%e A212808   14 0 1 0 0 0 2
%e A212808   42 0 2 3 0 1 4
%e A212808   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 A212808   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 A212808   ...
%Y A212808 Cf. A000108, A057545.
%K A212808 nonn,tabf
%O A212808 0,5
%A A212808 _N. J. A. Sloane_, May 29 2012