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A336269 Number of compositions of n containing no part p of multiplicity p.

%I A336269 #13 Mar 17 2022 14:53:21
%S A336269 1,0,2,2,5,11,18,36,84,155,305,625,1269,2487,5070,10263,20964,41905,
%T A336269 84799,170540,346192,696157,1405156,2822998,5686402,11420892,22949684,
%U A336269 46028648,92347798,185051670,370756866,742307736,1485798060,2972924906,5947567564
%N A336269 Number of compositions of n containing no part p of multiplicity p.
%H A336269 Alois P. Heinz, <a href="/A336269/b336269.txt">Table of n, a(n) for n = 0..1000</a>
%F A336269 a(n) = A011782(n) - A336273(n).
%p A336269 b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p A336269       add(`if`(i=j, 0, b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
%p A336269     end:
%p A336269 a:= n-> b(n$2, 0):
%p A336269 seq(a(n), n=0..40);
%t A336269 b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0,
%t A336269      Sum[If[i == j, 0, b[n - i*j, i - 1, p + j]/j!], {j, 0, n/i}]]];
%t A336269 a[n_] := b[n, n, 0];
%t A336269 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Mar 17 2022, after _Alois P. Heinz_ *)
%Y A336269 Cf. A011782, A242434, A276429, A336273.
%K A336269 nonn
%O A336269 0,3
%A A336269 _Alois P. Heinz_, Jul 15 2020