cp's OEIS Frontend

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

%I A321646 #10 Jan 22 2023 18:04:09
%S A321646 1,1,2,6,15,39,108,290,781,2050,5434,14210,37150,96347,248250,636278,
%T A321646 1620721,4108340,10361338,26016060,65019655,161831393,401090324,
%U A321646 990229108,2435316984,5967684036,14572351628,35464928382,86033632280,208062026930,501676936146
%N A321646 Number of distinct row/column permutations of Ferrers diagrams of integer partitions of n.
%F A321646 a(n) = Sum_{k = 1..A000041(n)} A008480(A215366(n,k)) * A008480(A122111(A215366(n,k))).
%e A321646 The a(4) = 15 diagrams:
%e A321646   o o o o
%e A321646 .
%e A321646   o o o   o o o   o o o   o o   o         o         o
%e A321646   o         o         o   o o   o o o   o o o   o o o
%e A321646 .
%e A321646   o o   o o   o     o       o     o
%e A321646   o       o   o o   o     o o     o
%e A321646   o       o   o     o o     o   o o
%e A321646 .
%e A321646   o
%e A321646   o
%e A321646   o
%e A321646   o
%t A321646 conj[y_]:=If[Length[y]==0,y,Table[Length[Select[y,#>=k&]],{k,1,Max[y]}]];
%t A321646 Table[Sum[Length[Permutations[y]]*Length[Permutations[conj[y]]],{y,IntegerPartitions[n]}],{n,10}]
%Y A321646 Cf. A000219, A008480, A049311, A068313, A101370, A120733, A122111, A321645, A321647, A321648, A321655.
%K A321646 nonn
%O A321646 0,3
%A A321646 _Gus Wiseman_, Nov 15 2018
%E A321646 a(11)-a(30) from _Alois P. Heinz_, Nov 15 2018