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A022815
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Number of terms in 5th derivative of a function composed with itself n times.
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2
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1, 7, 23, 55, 110, 196, 322, 498, 735, 1045, 1441, 1937, 2548, 3290, 4180, 5236, 6477, 7923, 9595, 11515, 13706, 16192, 18998, 22150, 25675, 29601, 33957, 38773, 44080, 49910, 56296, 63272, 70873, 79135, 88095, 97791, 108262, 119548, 131690
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n) = n*(n+1)*(n^2+13*n-2)/24. - John W. Layman (layman(AT)math.vt.edu), Apr 27 2000
G.f.: x*(1-2*x^2+2*x)/(1-x)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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PROG
| (MAGMA) [n*(n+1)*(n^2+13*n-2)/24: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011
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CROSSREFS
| Cf. A008778, A022811-A022818, A024207-A024210.
Sequence in context: A098334 A038796 A004068 * A172252 A027116 A151718
Adjacent sequences: A022812 A022813 A022814 * A022816 A022817 A022818
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
More terms from Christian G. Bower (bowerc(AT)usa.net), Aug 15 1999.
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