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A024210 Number of terms in n-th derivative of a function composed with itself 10 times. 12
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)
OFFSET

0,3

REFERENCES

W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.

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.

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)

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Last modified February 15 23:53 EST 2012. Contains 205860 sequences.