%I #11 May 20 2015 18:26:50
%S 1,30,210,867,2690,6956,15833,32775,63024,114235,197241,326976,523575,
%T 813671,1231910,1822706,2642259,3760860,5265508,7262865,9882576,
%U 13280982,17645255,23197985,30202250,38967201,49854195,63283510,79741677,99789465,124070556
%N Number of terms in 9th derivative of a function composed with itself n times.
%H Alois P. Heinz, <a href="/A215627/b215627.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 G.f.: (5*x^6-28*x^5+53*x^4-27*x^3-24*x^2+21*x+1)*x/(1-x)^9.
%F a(n) = n*(n+1)*(n^6+75*n^5+1703*n^4+13697*n^3+29472*n^2-30788*n+6000)/40320.
%p a:= n-> n*(n+1)*(6000+(-30788+(29472+(13697+(1703+(75+n)*n)*n)*n)*n)*n)/40320:
%p seq(a(n), n=1..40);
%Y Row n=9 of A022818.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Aug 18 2012