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 A024210 Number of terms in n-th derivative of a function composed with itself 10 times. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 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). CROSSREFS 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 KEYWORD nonn AUTHOR Winston C. Yang (yang(AT)math.wisc.edu) STATUS approved

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