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Search: id:A093637
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| A093637 |
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G.f.: A(x) = Product_{n>=0} 1/(1-a(n)*x^(n+1)) = Sum_{n>=0} a(n)*x^n. |
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+0
5
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| 1, 1, 2, 4, 9, 20, 49, 117, 297, 746, 1947, 5021, 13378, 35237, 95123, 254825, 694987, 1882707, 5184391, 14177587, 39289183, 108337723, 301997384, 837774846, 2347293253, 6546903307, 18417850843, 51617715836, 145722478875
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Comment from David Callan, Nov 02 2006: a(n) = number of (unlabeled, rooted) ordered trees on n edges such that, for each vertex of outdegree >= 1, the sizes of its subtrees are weakly increasing left to right. This notion is close to that of unlabeled, unordered rooted tree (A000081) but, for example,
./\...../\.
|./\.../\.|
|.........|
count as two different trees here whereas A000081 treats them as the same.
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EXAMPLE
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1/((1-x)(1-x^2)(1-2x^3)(1-4x^4)(1-9x^5)...) = 1 + x + 2x^2 + 4x^3 + 9x^4 + ...
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PROGRAM
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(PARI) a(n) = polcoeff(prod(i=0, n-1, 1/(1-a(i)*x^(i+1)))+x*O(x^n), n)
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CROSSREFS
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Cf. A000081, A093635, A093638.
Sequence in context: A145550 A000081 A124497 this_sequence A068051 A032289 A006648
Adjacent sequences: A093634 A093635 A093636 this_sequence A093638 A093639 A093640
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2004
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