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

1, 0, 2, 2, 5, 11, 18, 36, 84, 155, 305, 625, 1269, 2487, 5070, 10263, 20964, 41905, 84799, 170540, 346192, 696157, 1405156, 2822998, 5686402, 11420892, 22949684, 46028648, 92347798, 185051670, 370756866, 742307736, 1485798060, 2972924906, 5947567564

Offset: 0

Author

Alois P. Heinz, Jul 15 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A011782, A242434, A276429, A336273.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(`if`(i=j, 0, b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..40);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0,
     Sum[If[i == j, 0, b[n - i*j, i - 1, p + j]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 17 2022, after Alois P. Heinz *)

Formula

a(n) = A011782(n) - A336273(n).