A199885 - OEIS

%I #15 Nov 16 2014 15:05:17

%S 0,1,1,6,10,23,49,106,215,444,906,1849,3759,7621,15402,31091,62676,

%T 126206,253860,510204,1024665,2056608,4125625,8272436,16580967,

%U 33223336,66550937,133278720,266857006,534220745,1069297319,2140037990,4282507048,8569103770

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

%H Alois P. Heinz, <a href="/A199885/b199885.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^(n+1)-x)^d-(x^n-x)^d)/(x-1)^d).

%F a(n) = A000079(n-1) - A171632(n).

%e a(4) = 6: [1,1,1,1], [1,1,2], [1,2,1], [1,3], [2,1,1], [3,1].

%p 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 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 Cf. A000079, A171632, A200727.

%K nonn

%O 1,4

%A _Alois P. Heinz_, Nov 11 2011