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A319005 Number of integer partitions of n whose product of parts is >= n. 10
1, 1, 1, 1, 2, 2, 5, 7, 13, 18, 28, 40, 60, 80, 113, 152, 205, 266, 353, 454, 590, 751, 959, 1210, 1529, 1905, 2381, 2953, 3658, 4501, 5539, 6772, 8278, 10065, 12230, 14801, 17893, 21544, 25921, 31089, 37240, 44478, 53068, 63150, 75063, 89018, 105438, 124632 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

EXAMPLE

The a(1) = 1 through a(9) = 18 partitions:

  (1)  (2)  (3)  (4)   (5)   (6)    (7)     (8)      (9)

                 (22)  (32)  (33)   (43)    (44)     (54)

                             (42)   (52)    (53)     (63)

                             (222)  (322)   (62)     (72)

                             (321)  (331)   (332)    (333)

                                    (421)   (422)    (432)

                                    (2221)  (431)    (441)

                                            (521)    (522)

                                            (2222)   (531)

                                            (3221)   (621)

                                            (3311)   (3222)

                                            (4211)   (3321)

                                            (22211)  (4221)

                                                     (4311)

                                                     (5211)

                                                     (22221)

                                                     (32211)

                                                     (33111)

MAPLE

b:= proc(n, i, p) option remember; `if`(n=0 or i=1, `if`(p>1,

      0, 1), b(n, i-1, p) +b(n-i, min(i, n-i), max(p/i, 1)))

    end:

a:= n-> b(n$3):

seq(a(n), n=0..50);  # Alois P. Heinz, Oct 22 2018

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Times@@#>=n&]], {n, 50}]

CROSSREFS

Column sums of A319000.

Cf. A001055, A002865, A069016, A096276, A301987, A318950, A319057, A319916.

Sequence in context: A265795 A095295 A095333 * A095326 A095330 A036378

Adjacent sequences:  A319002 A319003 A319004 * A319006 A319007 A319008

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 22 2018

STATUS

approved

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)