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Search: id:A024208
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| A024208 |
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Number of terms in n-th derivative of a function composed with itself 8 times. |
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+0
3
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| 1, 1, 8, 36, 148, 498, 1590, 4586, 12644, 32775, 81901, 196085, 455772, 1025779, 2252674, 4823546, 10116553, 20783490, 41949270, 83211931, 162552093, 312850854, 594086542, 1113610526, 2062796698, 3777567977, 6844786250
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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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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-A024210. First column of A050302.
Sequence in context: A014477 A034998 A121255 this_sequence A000427 A000428 A083597
Adjacent sequences: A024205 A024206 A024207 this_sequence A024209 A024210 A024211
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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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