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 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. 0
 1, 2, 3, 2, 4, 2, 6, 1, 1, 5, 2, 6, 9, 1, 4, 4, 4, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are the Catalan numbers (A000108). Sum(k*A(n,k), k>0)=A014307(n). LINKS M. Klazar, Twelve countings with rooted plane trees, European Journal of Combinatorics 18 (1997), 195-210; Addendum, 18 (1997), 739-740. EXAMPLE We represent ordered trees by their corresponding Dyck paths via the "glove" bijection. The "tree" UDUUDD has 2 drawings: * , UD, UUDD, UDUUDD and *, UD, UDUD, UDUUDD; the "tree" UUDDUD has 2 drawings: *, UD, UUDD, UUDDUD and *, UD, UUDD, UUDDUD. Thus A(3,2)=2. The "tree" UUUDDD has 1 drawing: *, UD, UUDD, UUUDDD; the "tree" UUDUDD has 1 drawing: *, UD, UUDD, UUDUDD; the "tree" UDUDUD has 1 drawing: *, UD, UDUD, UDUDUD. Thus A(3,1)=3. Triangle starts: 1; 2; 3, 2; 4, 2, 6, 1, 1; 5, 2, 6, 9, 1, 4, 4, 4, 2, 1, 2, 2; CROSSREFS Sequence in context: A297162 A322587 A058973 * A235912 A277859 A308566 Adjacent sequences:  A155517 A155518 A155519 * A155521 A155522 A155523 KEYWORD more,nonn,tabf AUTHOR Emeric Deutsch, Mar 19 2009 EXTENSIONS Keyword tabf added by Michel Marcus, Apr 09 2013 STATUS approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)