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%I #14 Aug 02 2020 11:46:36
%S 1,22,129,468,1309,3101,6539,12644,22857,39148,64141,101256,154869,
%T 230491,334967,476696,665873,914754,1237945,1652716,2179341,2841465,
%U 3666499,4686044,5936345,7458776,9300357,11514304,14160613,17306679,21027951,25408624,30542369
%N Number of terms in 8th derivative of a function composed with itself n times.
%H Alois P. Heinz, <a href="/A215626/b215626.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.: (x^6-7*x^5+15*x^4-4*x^3-19*x^2+14*x+1)*x/(x-1)^8.
%F a(n) = n*(n+6)*(n^5+50*n^4+568*n^3+722*n^2-713*n+92)/5040.
%p a:= n-> n*(n+6)*(92+(-713+(722+(568+(50+n)*n)*n)*n)*n)/5040:
%p seq(a(n), n=1..40);
%t CoefficientList[Series[(x^6-7x^5+15x^4-4x^3-19x^2+14x+1)x/(x-1)^8,{x,0,40}],x]//Rest (* _Harvey P. Dale_, Aug 02 2020 *)
%Y Row n=8 of A022818.
%K nonn
%O 1,2
%A _Alois P. Heinz_, Aug 18 2012
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