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A022813
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Number of terms in n-th derivative of a function composed with itself 5 times.
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3
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1, 1, 5, 15, 45, 110, 271, 599, 1309, 2690, 5436, 10545, 20148, 37341, 68223, 121878, 214846, 371993, 636570, 1073325, 1790721, 2950922, 4816603, 7778937, 12455988, 19761148, 31108121, 48572686, 75307513, 115909727
(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 A039807.
Sequence in context: A076103 A094283 A158875 * A000334 A000335 A200465
Adjacent sequences: A022810 A022811 A022812 * A022814 A022815 A022816
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KEYWORD
| nonn
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AUTHOR
| Winston C. Yang (yang(AT)math.wisc.edu)
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