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%I #16 Nov 16 2014 15:04:34
%S 0,1,1,6,8,19,43,90,167,339,722,1503,2987,5883,11820,24167,49348,
%T 99707,199626,398475,797457,1604029,3237867,6534327,13143278,26336266,
%U 52664325,105349525,211135006,423949168,851981311,1711365899,3433202397,6878160656,13768314357
%N Number of compositions of n such that the number of parts is not divisible by the greatest part.
%H Alois P. Heinz, <a href="/A199884/b199884.txt">Table of n, a(n) for n = 1..250</a>
%F G.f.: Sum_{n>0} (2^(n-1)*x^n -Sum_{d|n} ((x^(d+1)-x)^n-(x^d-x)^n)/(x-1)^n).
%F a(n) = A000079(n-1) - A171634(n).
%e a(5) = 8: [1,2,2], [1,4], [2,1,2], [2,2,1], [2,3], [3,2], [4,1], [5].
%p b:= proc(n, t, g) option remember; `if`(n=0, `if`(irem(t, g)=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 b[n_, t_, g_] := b[n, t, g] = If[n == 0, If[Mod[t, g] == 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 Cf. A000079, A171634, A200727.
%K nonn
%O 1,4
%A _Alois P. Heinz_, Nov 11 2011
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