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A022811 Number of terms in n-th derivative of a function composed with itself 3 times. +0
15
1, 1, 3, 6, 13, 23, 44, 74, 129, 210, 345, 542, 858, 1310, 2004, 2996, 4467, 6540, 9552, 13744, 19711, 27943, 39452, 55172, 76865, 106200, 146173, 199806, 272075, 368247, 496642, 666201, 890602, 1184957, 1571417, 2075058, 2731677 (list; graph; listen)
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, A022812-A022818, A024207-A024210. First column of A039805.

A row or column of A081718.

Sequence in context: A019079 A048134 A058397 this_sequence A002799 A058554 A128517

Adjacent sequences: A022808 A022809 A022810 this_sequence A022812 A022813 A022814

KEYWORD

nonn

AUTHOR

Winston C. Yang (yang(AT)math.wisc.edu)

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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