

A022816


Number of terms in 6th derivative of a function composed with itself n times.


4



1, 11, 44, 121, 271, 532, 952, 1590, 2517, 3817, 5588, 7943, 11011, 14938, 19888, 26044, 33609, 42807, 53884, 67109, 82775, 101200, 122728, 147730, 176605, 209781, 247716, 290899, 339851, 395126, 457312, 527032, 604945, 691747
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OFFSET

1,2


REFERENCES

W. C. Yang (yang(AT)math.wisc.edu), Derivatives of selfcompositions of functions, preprint, 1997.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
W. C. Yang, Derivatives are essentially integer partitions, Discrete Mathematics, 222(13), July 2000, 235245.
Index entries for linear recurrences with constant coefficients, signature (6, 15, 20, 15, 6, 1).


FORMULA

a(n) = n*(n+1)*(n^3+24*n^2+81*n46)/120. G.f.: x*(1+5*x7*x^2+2*x^3)/(x1)^6.  R. J. Mathar, Sep 15 2009


MATHEMATICA

Table[n(n+1)(n^3+24n^2+81n46)/120, {n, 40}] (* or *) LinearRecurrence[{6, 15, 20, 15, 6, 1}, {1, 11, 44, 121, 271, 532}, 40] (* Harvey P. Dale, Dec 29 2017 *)


PROG

(MAGMA) [n*(n+1)*(n^3+24*n^2+81*n46)/120: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011


CROSSREFS

Cf. A008778, A022811A022818, A024207A024210.
Sequence in context: A111080 A299288 A299286 * A120537 A068596 A002089
Adjacent sequences: A022813 A022814 A022815 * A022817 A022818 A022819


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Christian G. Bower, Aug 15 1999.


STATUS

approved



