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Search: id:A024207
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| A024207 |
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Number of terms in n-th derivative of a function composed with itself 7 times. |
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+0
13
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| 1, 1, 7, 28, 105, 322, 952, 2541, 6539, 15833, 37148, 83594, 183289, 389520, 809820, 1643375, 3272797, 6390745, 12279337, 23208483, 43252360, 79483096, 144265338, 258673983, 458747540, 804877837, 1398356706, 2406328974
(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-A022817, A024208-A024210. First column of A050301.
Sequence in context: A054469 A117473 A022572 this_sequence A000416 A000417 A026642
Adjacent sequences: A024204 A024205 A024206 this_sequence A024208 A024209 A024210
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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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