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Search: id:A024209
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| A024209 |
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Number of terms in n-th derivative of a function composed with itself 9 times. |
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+0
3
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| 1, 1, 9, 45, 201, 735, 2517, 7785, 22857, 63024, 166819, 422537, 1035971, 2456694, 5672347, 12756334, 28053280, 60371967, 127479247, 264311585, 539102751, 1082474167, 2142579168, 4183251750, 8064722973, 15360809911
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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-A022817, A024207-A024210. First column of A050303.
Sequence in context: A050574 A124647 A111640 this_sequence A026092 A054628 A132133
Adjacent sequences: A024206 A024207 A024208 this_sequence A024210 A024211 A024212
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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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