%I #7 Feb 10 2015 04:01:00
%S 1,0,0,0,0,0,0,0,1,9,45,165,495,1287,3003,6435,12871,24319,43812,
%T 75837,127005,207252,332343,529617,851797,1410484,2456794,4572624,
%U 9116790,19248417,42237738,94608183,213426424,480788350,1076330078,2388681769,5249788389
%N Number of compositions of n with exactly eight occurrences of the largest part.
%H Joerg Arndt and Alois P. Heinz, <a href="/A243743/b243743.txt">Table of n, a(n) for n = 8..650</a>
%p b:= proc(n, p, i) option remember; `if`(n=0, p!,
%p `if`(i<1, 0, add(b(n-i*j, p+j, i-1)/j!, j=0..n/i)))
%p end:
%p a:= proc(n) local k; k:=8;
%p add(b(n-i*k, k, i-1)/k!, i=1..n/k)
%p end:
%p seq(a(n), n=8..50);
%t b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_] := (k=8; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 8, 50}] (* _Jean-François Alcover_, Feb 10 2015, after Maple *)
%Y Column k=8 of A238341.
%K nonn
%O 8,10
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 09 2014