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A024210
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Number of terms in n-th derivative of a function composed with itself 10 times.
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12
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1, 1, 10, 55, 265, 1045, 3817, 12583, 39148, 114235, 318857, 850576, 2190850, 5451721, 13184711, 31023842, 71286349, 160139911, 352574213, 761567304, 1616713932, 3376143283, 6944345483, 14080091227, 28169087367
(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-A022817, A024207-A024209. First column of A050304.
Sequence in context: A022575 A202481 A169720 * A188168 A199413 A054629
Adjacent sequences: A024207 A024208 A024209 * A024211 A024212 A024213
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KEYWORD
| nonn
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AUTHOR
| Winston C. Yang (yang(AT)math.wisc.edu)
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