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Search: id:A113822
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| A113822 |
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Number of binary trees of weight n where leaves have positive integer weights, where the order of subtrees is insignificant. Commutative non-associative version of partitions of n. |
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+0
1
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| 1, 1, 2, 3, 7, 14, 35, 85, 226, 600, 1658, 4622, 13141, 37699, 109419, 320017, 943329, 2797788, 8346030, 25019401, 75340824, 227777899, 691146578, 2104028507, 6424449318, 19670277332, 60378290912, 185763773723, 572764664975
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(2n) = 1 + C(a(n)+1, 2) + sum_{k=1}^{n/2-1} a(k)*a(2n-k). a(2n+1) = 1 + sum_{k=1}^{(n-1)/2} a(k)*a(2n+1-k), with a(0)=0.
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EXAMPLE
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For a(4)=7, we have the following 7 sums: 4, 3+1, 2+2, (2+1)+1, (1+1)+2, ((1+1)+1)+1, (1+1)+(1+1).
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CROSSREFS
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Cf. A007317, A000041.
Sequence in context: A103421 A000642 A035083 this_sequence A036250 A006660 A123777
Adjacent sequences: A113819 A113820 A113821 this_sequence A113823 A113824 A113825
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KEYWORD
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easy,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 23 2006
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