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%I #5 May 29 2014 18:52:54
%S 1,0,9,9,54,99,309,684,1720,3918,9081,20343,45261,99063,214719,460428,
%T 965980,2040096,4255851,8706522,17810088,36275538,73017027,145692324,
%U 289702678,573412764,1124242476,2191850439,4259718588,8229423030,15785908575,30199934205
%N Number of compositions of n in which the maximal multiplicity of parts equals 8.
%H Alois P. Heinz, <a href="/A243125/b243125.txt">Table of n, a(n) for n = 8..1000</a>
%F a(n) = A243086(n) - A243085(n) = A243081(n,8) - A243081(n,7).
%p b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
%p end:
%p a:= n-> b(n$2, 0, 8) -b(n$2, 0, 7):
%p seq(a(n), n=8..50);
%Y Column k=8 of A242447.
%K nonn
%O 8,3
%A _Alois P. Heinz_, May 29 2014