A350788 Irregular triangle read by rows: T(n,k) is the number of partial functions on [n] such that the sizes of the preimages of the individual elements in the range form the k-th partition in the class of all partitions listed in canonical (graded reverse lexicographic) order, n>=0, 0<=k<=A000070(n).

1, 1, 1, 1, 4, 2, 2, 1, 9, 9, 18, 3, 18, 6, 1, 16, 24, 72, 16, 144, 96, 4, 48, 36, 144, 24, 1, 25, 50, 200, 50, 600, 600, 25, 400, 300, 1800, 600, 5, 100, 200, 600, 900, 1200, 120, 1, 36, 90, 450, 120, 1800, 2400, 90, 1800, 1350, 10800, 5400, 36, 900, 1800, 7200, 10800, 21600, 4320, 6, 180, 450, 1800, 300, 7200, 7200, 1800, 16200, 10800, 720

Offset

0,5

Comments

Row sums are (n+1)^n = A000169(n+1).

Links

Table of n, a(n) for n=0..74.

OEIS Wiki, Orderings of partitions (a comparison).

Example

Triangle begins:
  1,
  1,  1,
  1,  4,  2,  2,
  1,  9,  9, 18,  3,  18,  6,
  1, 16, 24, 72, 16, 144, 96, 4, 48, 36, 144, 24

Mathematica

g[n_, list_] := Multinomial @@ Join[{n - Length[list]}, Table[Count[list, i], {i, 1, n}]]* Multinomial @@ Join[{n - Total[list]}, list]; Table[Map[g[nn, #] &,
   Level[Table[IntegerPartitions[k], {k, 0, nn}], {2}]], {nn, 0, 5}] // Grid

Crossrefs

Cf. A000169, A049009, A000041, A000070, A080577.

Sequence in context: A102888 A071558 A179621 * A282698 A136709 A254969

Adjacent sequences: A350785 A350786 A350787 * A350789 A350790 A350791

Keyword

nonn,tabf

Author

Geoffrey Critzer, Jan 16 2022

Extensions

Name corrected by Geoffrey Critzer, Jan 17 2026

Status

approved