A022816 Number of terms in 6th derivative of a function composed with itself n times.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions 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(1-3), July 2000, 235-245.
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A008778, A022811-A022818, A024207-A024210.

Programs

Magma

[n*(n+1)*(n^3+24*n^2+81*n-46)/120: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011

Mathematica

Table[n(n+1)(n^3+24n^2+81n-46)/120,{n,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,11,44,121,271,532},40] (* Harvey P. Dale, Dec 29 2017 *)

PARI

a(n)=n*(n+1)*(n^3+24*n^2+81*n-46)/120 \\ Charles R Greathouse IV, Oct 21 2022

Formula

a(n) = n*(n+1)*(n^3+24*n^2+81*n-46)/120. G.f.: x*(1+5*x-7*x^2+2*x^3)/(x-1)^6. - R. J. Mathar, Sep 15 2009

Extensions

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