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A199885 Number of compositions of n such that the greatest part is not divisible by the number of parts.

%I A199885 #15 Nov 16 2014 15:05:17
%S A199885 0,1,1,6,10,23,49,106,215,444,906,1849,3759,7621,15402,31091,62676,
%T A199885 126206,253860,510204,1024665,2056608,4125625,8272436,16580967,
%U A199885 33223336,66550937,133278720,266857006,534220745,1069297319,2140037990,4282507048,8569103770
%N A199885 Number of compositions of n such that the greatest part is not divisible by the number of parts.
%H A199885 Alois P. Heinz, <a href="/A199885/b199885.txt">Table of n, a(n) for n = 1..250</a>
%F A199885 G.f.: Sum_{n>0} (2^(n-1)*x^n-Sum_{d|n} ((x^(n+1)-x)^d-(x^n-x)^d)/(x-1)^d).
%F A199885 a(n) = A000079(n-1) - A171632(n).
%e A199885 a(4) = 6: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1].
%p A199885 b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(g, t)=0, 0, 1), add(b(n-i, t+1, max(i, g)), i=1..n)) end: a:= n-> b(n, 0, 0): seq(a(n), n=1..40);
%t A199885 b[n_, t_, g_] := b[n, t, g] = If[n == 0, If[Mod[g, t] == 0, 0, 1], Sum [b[n-i, t+1, Max[i, g]], {i, 1, n}]]; a[n_] := b[n, 0, 0]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Nov 05 2014, after _Alois P. Heinz_ *)
%Y A199885 Cf. A000079, A171632, A200727.
%K A199885 nonn
%O A199885 1,4
%A A199885 _Alois P. Heinz_, Nov 11 2011