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A120803
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Number of series-reduced balanced trees with n leaves.
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0
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1, 1, 1, 2, 2, 4, 4, 8, 9, 16, 20, 37, 47, 80, 111, 183, 256, 413, 591, 940, 1373, 2159, 3214, 5067, 7649, 12054, 18488, 29203, 45237, 71566, 111658, 176710, 276870, 437820, 687354, 1085577, 1705080, 2688285, 4221333, 6644088, 10425748
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| In other words, rooted trees with all leaves at the same level and no node having exactly one child; the order of children is not significant.
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FORMULA
| Let s_0(n) = 1 if n = 1, 0 otherwise; s_{k+1}(n) = EULER(s_k)(n) - s_k(n), where EULER is the Euler transform. Then a_n = sum_k s_k(n). (s_k(n) is the number of such trees of height k.) Note that s_k(n) = 0 for n < 2^k.
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CROSSREFS
| Cf. A119262, A007059, A000669, A001003.
Sequence in context: A060546 A163403 A183565 * A000011 A187213 A022476
Adjacent sequences: A120800 A120801 A120802 * A120804 A120805 A120806
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KEYWORD
| nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 18 2006
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