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

Author

Gus Wiseman, Nov 15 2018

Keywords

• nonn

Examples

			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
		

Crossrefs

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

Programs

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}]

Formula

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

Extensions

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