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A114324 Number of partitions of n with a product greater than n. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified November 20 13:03 EST 2019. Contains 329336 sequences. (Running on oeis4.)