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

0,3

Links

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

Formula

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

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<m, 1, `if`(j=m, t+1, t))), j=1..n/i)))
    end:
a:= n-> 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 *)

Crossrefs

Cf. A000041, A003056, A362615, A372542.

Sequence in context: A352359 A372542 A226007 * A257655 A318026 A173241

Adjacent sequences: A372629 A372630 A372631 * A372633 A372634 A372635

Keyword

nonn

Author

Alois P. Heinz, May 07 2024

Status

approved