A022816 - OEIS

%I #25 Oct 21 2022 21:56:14

%S 1,11,44,121,271,532,952,1590,2517,3817,5588,7943,11011,14938,19888,

%T 26044,33609,42807,53884,67109,82775,101200,122728,147730,176605,

%U 209781,247716,290899,339851,395126,457312,527032,604945,691747

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

%D W. C. Yang (yang(AT)math.wisc.edu), Derivatives of self-compositions of functions, preprint, 1997.

%H Vincenzo Librandi, <a href="/A022816/b022816.txt">Table of n, a(n) for n = 1..10000</a>

%H W. C. Yang, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00412-4">Derivatives are essentially integer partitions</a>, Discrete Mathematics, 222(1-3), July 2000, 235-245.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).

%F 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

%t 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 *)

%o (Magma) [n*(n+1)*(n^3+24*n^2+81*n-46)/120: n in [1..40]]; // _Vincenzo Librandi_, Oct 10 2011

%o (PARI) a(n)=n*(n+1)*(n^3+24*n^2+81*n-46)/120 \\ _Charles R Greathouse IV_, Oct 21 2022

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

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Christian G. Bower_, Aug 15 1999.