A325039 Number of integer partitions of n with the same product of parts as their conjugate.

1, 1, 0, 1, 1, 1, 1, 1, 6, 2, 2, 4, 3, 5, 7, 6, 5, 7, 9, 10, 11, 18, 16, 19, 19, 16, 20, 20, 28, 39, 28, 40, 53, 45, 52, 59, 71, 61, 73, 97, 102, 95, 112, 131, 137, 148, 140, 166, 199, 181, 238, 251, 255, 289, 339, 344, 381, 398, 422, 464, 541, 555, 628, 677, 732

Offset: 0

Author

Gus Wiseman, Mar 25 2019

Keywords

• nonn

Comments

For example, the partition (6,4,1) with product 24 has conjugate (3,2,2,2,1,1) with product also 24.

The Heinz numbers of these partitions are given by A325040.

Examples

			The a(8) = 6 through a(15) = 6 integer partitions:
  (44)    (333)    (4321)   (641)     (4422)    (4432)     (6431)
  (332)   (51111)  (52111)  (4331)    (53211)   (6421)     (8411)
  (431)                     (322211)  (621111)  (53311)    (54221)
  (2222)                    (611111)            (432211)   (433211)
  (3221)                                        (7111111)  (632111)
  (4211)                                                   (7211111)
                                                           (42221111)
		

Crossrefs

Cf. A001055, A064573, A122111, A296150, A318950, A319000, A320322, A321649.

Cf. A325040, A325041, A325042, A325045.

Programs

Mathematica

conj[y_]:=If[Length[y]==0,y,Table[Length[Select[y,#>=k&]],{k,1,Max[y]}]];
Table[Length[Select[IntegerPartitions[n],Times@@#==Times@@conj[#]&]],{n,0,30}]

Extensions

More terms from Jinyuan Wang, Jun 27 2020