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Search: id:A022813
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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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+0
4
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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; 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 A039807.
Sequence in context: A076103 A094283 A158875 this_sequence A000334 A000335 A005030
Adjacent sequences: A022810 A022811 A022812 this_sequence A022814 A022815 A022816
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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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