A326152 Number of integer partitions of n whose product of parts is 2 * n.

0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 0, 5, 0, 2, 3, 5, 0, 7, 0, 5, 3, 2, 0, 10, 2, 2, 5, 5, 0, 9, 0, 9, 3, 2, 3, 14, 0, 2, 3, 10, 0, 9, 0, 5, 9, 2, 0, 17, 2, 7, 3, 5, 0, 14, 3, 10, 3, 2, 0, 19, 0, 2, 9, 13, 3, 9, 0, 5, 3, 9, 0, 27, 0, 2, 9, 5, 3, 9, 0, 17, 10, 2, 0

Offset: 0

Author

Gus Wiseman, Jun 09 2019

Keywords

• nonn

Comments

Also the number of orderless factorizations of 2 * n into factors > 1 with sum at most n.

The Heinz numbers of these partitions are given by A326151.

Examples

			The a(8) = 3 through a(16) = 5 partitions (empty columns not shown) (A = 10):
  (44)    (63)    (541)   (831)      (74111)   (A311)      (841111)
  (422)   (3321)  (5221)  (6411)     (722111)  (651111)    (8221111)
  (2222)                  (62211)              (53211111)  (442111111)
                          (432111)                         (4222111111)
                          (3222111)                        (22222111111)
		

Crossrefs

Cf. A003963, A057567, A057568, A096276, A114324, A301987, A319005, A326149, A326151, A326156, A326157.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],Times@@#==2*n&]],{n,0,30}]