A022817 - OEIS

%I #26 May 20 2015 18:28:09

%S 1,15,74,237,599,1301,2541,4586,7785,12583,19536,29327,42783,60893,

%T 84827,115956,155873,206415,269686,348081,444311,561429,702857,872414,

%U 1074345,1313351,1594620,1923859,2307327,2751869,3264951,3854696,4529921,5300175,6175778

%N Number of terms in 7th 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 Alois P. Heinz, <a href="/A022817/b022817.txt">Table of n, a(n) for n = 1..1000</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.

%F a(n) = n/720 * (n^5 + 39*n^4 + 355*n^3 + 645*n^2 - 356*n + 36).

%F G.f.: (x^5-4*x^4+x^3+10*x^2-8*x-1)*x/(x-1)^7. - _Alois P. Heinz_, Aug 18 2012

%p a:= n-> n*(36+(-356+(645+(355+(39+n)*n)*n)*n)*n)/720:

%p seq(a(n), n=1..40);  # _Alois P. Heinz_, Aug 18 2012

%t Table[(n/720*(n^5+39*n^4+355*n^3+645*n^2-356*n+36)),{n,1,100}] (* _Vincenzo Librandi_, Aug 18 2012 *)

%Y Cf. A008778, A022811-A022816, A024207-A024210.

%Y Row n=4 of A022818.

%K nonn

%O 1,2

%A _N. J. A. Sloane_.

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