A022814 Number of terms in n-th derivative of a function composed with itself 6 times.
1, 1, 6, 21, 71, 196, 532, 1301, 3101, 6956, 15217, 31951, 65670, 130914, 256150, 489690, 920905, 1699693, 3092751, 5540571, 9802091, 17114237, 29550346, 50444952, 85264328, 142682505, 236649524, 389033014, 634408230, 1026350152, 1648328017, 2628254619
Offset: 0
Keywords
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.
Programs
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Mathematica
b[n_, i_, k_] := b[n, i, k] = If[n
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).