A321646 Number of distinct row/column permutations of Ferrers diagrams of integer partitions of n.

1, 1, 2, 6, 15, 39, 108, 290, 781, 2050, 5434, 14210, 37150, 96347, 248250, 636278, 1620721, 4108340, 10361338, 26016060, 65019655, 161831393, 401090324, 990229108, 2435316984, 5967684036, 14572351628, 35464928382, 86033632280, 208062026930, 501676936146

Offset

0,3

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = Sum_{k = 1..A000041(n)} A008480(A215366(n,k)) * A008480(A122111(A215366(n,k))).

Example

The a(4) = 15 diagrams:
  o o o o
.
  o o o   o o o   o o o   o o   o         o         o
  o         o         o   o o   o o o   o o o   o o o
.
  o o   o o   o     o       o     o
  o       o   o o   o     o o     o
  o       o   o     o o     o   o o
.
  o
  o
  o
  o

Mathematica

conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Table[Sum[Length[Permutations[y]]*Length[Permutations[conj[y]]], {y, IntegerPartitions[n]}], {n, 10}]

Crossrefs

Cf. A000219, A008480, A049311, A068313, A101370, A120733, A122111, A321645, A321647, A321648, A321655.

Sequence in context: A001674 A121331 A026270 * A246563 A259399 A307128

Adjacent sequences: A321643 A321644 A321645 * A321647 A321648 A321649

Keyword

nonn

Author

Gus Wiseman, Nov 15 2018

Extensions

a(11)-a(30) from Alois P. Heinz, Nov 15 2018

Status

approved