cp's OEIS Frontend

A155520 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.

%I A155520 #7 Feb 07 2018 16:02:59
%S A155520 1,2,3,2,4,2,6,1,1,5,2,6,9,1,4,4,4,2,1,2,2
%N A155520 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 A155520 Row sums are the Catalan numbers (A000108).
%C A155520 Sum(k*A(n,k), k>0)=A014307(n).
%H A155520 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 A155520 We represent ordered trees by their corresponding Dyck paths via the "glove" bijection.
%e A155520 The "tree" UDUUDD has 2 drawings:
%e A155520 * , UD, UUDD, UDUUDD and *, UD, UDUD, UDUUDD;
%e A155520 the "tree" UUDDUD has 2 drawings:
%e A155520 *, UD, UUDD, UUDDUD and *, UD, UUDD, UUDDUD.
%e A155520 Thus A(3,2)=2.
%e A155520 The "tree" UUUDDD has 1 drawing: *, UD, UUDD, UUUDDD;
%e A155520 the "tree" UUDUDD has 1 drawing: *, UD, UUDD, UUDUDD;
%e A155520 the "tree" UDUDUD has 1 drawing: *, UD, UDUD, UDUDUD.
%e A155520 Thus A(3,1)=3.
%e A155520 Triangle starts:
%e A155520 1;
%e A155520 2;
%e A155520 3, 2;
%e A155520 4, 2, 6, 1, 1;
%e A155520 5, 2, 6, 9, 1, 4, 4, 4, 2, 1, 2, 2;
%K A155520 more,nonn,tabf
%O A155520 1,2
%A A155520 _Emeric Deutsch_, Mar 19 2009
%E A155520 Keyword tabf added by _Michel Marcus_, Apr 09 2013