A372632 Sum over all partitions of n of the number of elements with minimal multiplicity in their partition.

0, 1, 2, 4, 6, 9, 16, 21, 33, 47, 67, 90, 134, 172, 242, 321, 434, 558, 761, 961, 1279, 1627, 2112, 2657, 3452, 4292, 5481, 6824, 8619, 10634, 13381, 16389, 20425, 24989, 30864, 37556, 46221, 55912, 68337, 82510, 100262, 120476, 145855, 174562, 210272, 251065

Offset: 0

Author

Alois P. Heinz, May 07 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A000041, A003056, A362615, A372542.

Programs

Maple

b:= proc(n, i, m, t) option remember; `if`(n=0, t,
      `if`(i<1, 0, b(n, i-1, m, t)+add(b(n-i*j, i-1, min(j, m),
      `if`(j b(n$3, 0):
seq(a(n), n=0..45);

Mathematica

b[n_, i_, m_, t_] := b[n, i, m, t] = If[n == 0, t,
   If[i < 1, 0, b[n, i - 1, m, t] + Sum[b[n - i*j, i - 1, Min[j, m],
   If[j < m, 1, If[j == m, t + 1, t]]], {j, 1, n/i}]]];
a[n_] := b[n, n, n, 0];
Table[a[n], {n, 0, 45}] (* Jean-François Alcover, May 10 2024, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..A003056(n)} k * A362615(n,k).