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 A024209 Number of terms in n-th derivative of a function composed with itself 9 times. 5
 1, 1, 9, 45, 201, 735, 2517, 7785, 22857, 63024, 166819, 422537, 1035971, 2456694, 5672347, 12756334, 28053280, 60371967, 127479247, 264311585, 539102751, 1082474167, 2142579168, 4183251750, 8064722973, 15360809911, 28928858208, 53896616704, 99398216733 (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..1000 W. C. Yang, Derivatives are essentially integer partitions, Discrete Mathematics, 222(1-3), July 2000, 235-245. 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). MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n

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Last modified April 20 22:39 EDT 2021. Contains 343140 sequences. (Running on oeis4.)