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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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4
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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.
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FORMULA
| 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
| Cf. A008778, A022811-A022818, A024207-A024210. First column of A039806.
Sequence in context: A145775 A001214 A200455 * A192306 A000293 A000294
Adjacent sequences: A022809 A022810 A022811 * A022813 A022814 A022815
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KEYWORD
| nonn
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AUTHOR
| Winston C. Yang (yang(AT)math.wisc.edu)
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