A350650 Number of partitions of [n] having exactly one block containing its own index when blocks are ordered with decreasing largest elements.

0, 1, 1, 3, 7, 25, 91, 390, 1797, 9069, 49106, 284537, 1751554, 11406588, 78254594, 563642925, 4249337018, 33443545866, 274130245342, 2335311549498, 20637538548167, 188867393030394, 1787189672368355, 17461684290203403, 175930808241047092, 1825666076751872506

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Example

a(4) = 7: 4321, 43|21, 43|2|1, 421|3, 4|321, 4|32|1, 41|3|2.

Maple

b:= proc(n, m) option remember; series(`if`(n=0, 1, add(
      `if`(j=n, x, 1)*b(n-1, max(m, j)), j=1..m+1)), x, 2)
    end:
a:= n-> coeff(b(n, 0), x, 1):
seq(a(n), n=0..25);

Mathematica

b[n_, m_] := b[n, m] = Series[If[n == 0, 1, Sum[
    If[j == n, x, 1]*b[n-1, Max[m, j]], {j, 1, m+1}]], {x, 0, 2}];
a[n_] := Coefficient[b[n, 0], x, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 16 2022, after Alois P. Heinz *)

Crossrefs

Column k=1 of A350647, A350684.

Sequence in context: A343278 A002870 A096579 * A120540 A176829 A352385

Adjacent sequences: A350647 A350648 A350649 * A350651 A350652 A350653

Keyword

nonn

Author

Alois P. Heinz, Jan 09 2022

Status

approved