A155520 - OEIS

%I #7 Feb 07 2018 16:02:59

%S 1,2,3,2,4,2,6,1,1,5,2,6,9,1,4,4,4,2,1,2,2

%N Triangle read by rows: A(n,k) is the number of ordered trees with n edges having k drawings. A drawing of an ordered tree T with n edges is a sequence of trees (T_0, T_1, T_2, ..., T_n), such that T_n = T and T_{i-1} arises from T_i by deleting a leaf of T_i.

%C Row sums are the Catalan numbers (A000108).

%C Sum(k*A(n,k), k>0)=A014307(n).

%H M. Klazar, <a href="http://dx.doi.org/10.1006/eujc.1995.0095">Twelve countings with rooted plane trees</a>, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740.

%e We represent ordered trees by their corresponding Dyck paths via the "glove" bijection.

%e The "tree" UDUUDD has 2 drawings:

%e * , UD, UUDD, UDUUDD and *, UD, UDUD, UDUUDD;

%e the "tree" UUDDUD has 2 drawings:

%e *, UD, UUDD, UUDDUD and *, UD, UUDD, UUDDUD.

%e Thus A(3,2)=2.

%e The "tree" UUUDDD has 1 drawing: *, UD, UUDD, UUUDDD;

%e the "tree" UUDUDD has 1 drawing: *, UD, UUDD, UUDUDD;

%e the "tree" UDUDUD has 1 drawing: *, UD, UDUD, UDUDUD.

%e Thus A(3,1)=3.

%e Triangle starts:

%e 1;

%e 2;

%e 3, 2;

%e 4, 2, 6, 1, 1;

%e 5, 2, 6, 9, 1, 4, 4, 4, 2, 1, 2, 2;

%K more,nonn,tabf

%O 1,2

%A _Emeric Deutsch_, Mar 19 2009

%E Keyword tabf added by _Michel Marcus_, Apr 09 2013