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Search: id:A022812
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| A022812 |
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Number of terms in n-th derivative of a function composed with itself 4 times. |
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+0
5
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| 1, 1, 4, 10, 26, 55, 121, 237, 468, 867, 1597, 2821, 4952, 8421, 14206, 23439, 38324, 61570, 98112, 154111, 240197, 370015, 565802, 856664, 1288366, 1921016, 2846572, 4186730, 6122369, 8893904, 12851713, 18460961, 26388354
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.
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FORMULA
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If a(n, m) = number of terms in m-derivative of a function composed with itself n times, p(n, k) = number of partitions of n into k parts, then a(n, m)=sum{i=0..m}p(m, i)a(n-1, i).
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CROSSREFS
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Cf. A008778, A022811-A022818, A024207-A024210. First column of A039806.
Sequence in context: A097136 A049348 A001214 this_sequence A000293 A000294 A133086
Adjacent sequences: A022809 A022810 A022811 this_sequence A022813 A022814 A022815
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KEYWORD
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nonn
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AUTHOR
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Winston C. Yang (yang(AT)math.wisc.edu)
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