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Search: id:A136629
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| A136629 |
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Number of labeled PQ-trees with n leaves. |
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+0
1
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| 0, 1, 1, 7, 68, 941, 16657, 360151, 9197036, 270900242, 9041240104, 337195959574, 13898017639838, 627328651766168, 30776662410513268, 1630608894822320320, 92788669297928611880, 5644035534941116506704
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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A PQ-tree is a rooted tree with P-type internal nodes that have at least 3 children that are reversibly ordered (the reverse of the order is equivalent to the order) and Q-type internal nodes that have at least 2 unordered children.
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 242 (3.3.91)
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LINKS
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Christian G. Bower, Table of n, a(n) for n = 0..127
Index entries for sequences related to rooted trees
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FORMULA
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E.g.f. satisfies A(x) = x + 1/(2-2A(x)) + exp(A(x)) - A(x)^2/2 - 3/2*(A(x)+1)
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PROGRAM
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(PARI) read("transforms_pari.txt"); {pql(A) = A = trv_chain_l(A)+trv_exp(A)-opv_mul_egf(A, A)/2-2*A; A[1]=0; A} {apql(n) = local(SX, SY); SY = SX = [0, 1]; for(i=1, n, SY=concat(SY, 0); SX=concat(SX, 0); SY=SX+pql(SY)); SY} A136629(n) = apql(min(1, n-1))[n+1]
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CROSSREFS
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Sequence in context: A093170 A120079 A087567 this_sequence A133697 A122010 A084774
Adjacent sequences: A136626 A136627 A136628 this_sequence A136630 A136631 A136632
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Jan 14 2008
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