A114324 Number of partitions of n with a product greater than n.

1, 0, 0, 0, 0, 1, 3, 6, 10, 16, 26, 39, 56, 79, 111, 150, 200, 265, 349, 453, 586, 749, 957, 1209, 1522, 1903, 2379, 2950, 3654, 4500, 5534, 6771, 8271, 10063, 12228, 14799, 17884, 21543, 25919, 31087, 37233, 44477, 53063, 63149, 75059, 89014, 105436, 124631

Offset

0,7

Comments

The Heinz numbers of these partitions are given by A325037. - Gus Wiseman, Mar 27 2019

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Pankaj Jyoti Mahanta, On the number of partitions of n whose product of the summands is at most n, arXiv:2010.07353 [math.CO], 2020.

Example

a(6) = 3 since there are 3 partitions of 6 with product greater than 6: {3,3}, {2,2,2}, {4,2}.
From Gus Wiseman, Mar 27 2019: (Start)
The a(5) = 1 through a(9) = 16 partitions:
  (32)  (33)   (43)    (44)    (54)
        (42)   (52)    (53)    (63)
        (222)  (322)   (62)    (72)
               (331)   (332)   (333)
               (421)   (422)   (432)
               (2221)  (431)   (441)
                       (521)   (522)
                       (2222)  (531)
                       (3221)  (621)
                       (3311)  (3222)
                               (3321)
                               (4221)
                               (4311)
                               (5211)
                               (22221)
                               (32211)
(End)

Mathematica

<< DiscreteMath`Combinatorica`; lst=Table[Length@Select[Partitions[n], (Times @@ # > n) &], {n, 50}]
Table[Length[Select[IntegerPartitions[n], Times@@#>n&]], {n, 0, 20}] (* Gus Wiseman, Mar 27 2019 *)

Crossrefs

Cf. A001055, A028422, A096276, A114324, A301987, A319000, A319005, A319916, A325037, A325038, A325044.

Sequence in context: A265072 A152009 A255875 * A265073 A265074 A054886

Adjacent sequences: A114321 A114322 A114323 * A114325 A114326 A114327

Keyword

nonn

Author

Giovanni Resta, Feb 06 2006

Extensions

a(0) = 1 prepended by Gus Wiseman, Mar 27 2019

Status

approved