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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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14
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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, 55644767253, 108617341172, 209626751905
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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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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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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-A024209. First column of A050304.
Column k=10 of A022818.
Sequence in context: A022575 A202481 A169720 * A188168 A199413 A054629
Adjacent sequences: A024207 A024208 A024209 * A024211 A024212 A024213
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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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STATUS
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approved
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