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Search: id:A022811
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| A022811 |
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Number of terms in n-th derivative of a function composed with itself 3 times. |
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+0
15
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| 1, 1, 3, 6, 13, 23, 44, 74, 129, 210, 345, 542, 858, 1310, 2004, 2996, 4467, 6540, 9552, 13744, 19711, 27943, 39452, 55172, 76865, 106200, 146173, 199806, 272075, 368247, 496642, 666201, 890602, 1184957, 1571417, 2075058, 2731677
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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, A022812-A022818, A024207-A024210. First column of A039805.
A row or column of A081718.
Sequence in context: A019079 A048134 A058397 this_sequence A002799 A058554 A128517
Adjacent sequences: A022808 A022809 A022810 this_sequence A022812 A022813 A022814
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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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