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

%I A114324 #16 Oct 16 2020 10:01:25
%S A114324 1,0,0,0,0,1,3,6,10,16,26,39,56,79,111,150,200,265,349,453,586,749,
%T A114324 957,1209,1522,1903,2379,2950,3654,4500,5534,6771,8271,10063,12228,
%U A114324 14799,17884,21543,25919,31087,37233,44477,53063,63149,75059,89014,105436,124631
%N A114324 Number of partitions of n with a product greater than n.
%C A114324 The Heinz numbers of these partitions are given by A325037. - _Gus Wiseman_, Mar 27 2019
%H A114324 Alois P. Heinz, <a href="/A114324/b114324.txt">Table of n, a(n) for n = 0..1000</a>
%H A114324 Pankaj Jyoti Mahanta, <a href="https://arxiv.org/abs/2010.07353">On the number of partitions of n whose product of the summands is at most n</a>, arXiv:2010.07353 [math.CO], 2020.
%e A114324 a(6) = 3 since there are 3 partitions of 6 with product greater than 6: {3,3}, {2,2,2}, {4,2}.
%e A114324 From _Gus Wiseman_, Mar 27 2019: (Start)
%e A114324 The a(5) = 1 through a(9) = 16 partitions:
%e A114324   (32)  (33)   (43)    (44)    (54)
%e A114324         (42)   (52)    (53)    (63)
%e A114324         (222)  (322)   (62)    (72)
%e A114324                (331)   (332)   (333)
%e A114324                (421)   (422)   (432)
%e A114324                (2221)  (431)   (441)
%e A114324                        (521)   (522)
%e A114324                        (2222)  (531)
%e A114324                        (3221)  (621)
%e A114324                        (3311)  (3222)
%e A114324                                (3321)
%e A114324                                (4221)
%e A114324                                (4311)
%e A114324                                (5211)
%e A114324                                (22221)
%e A114324                                (32211)
%e A114324 (End)
%t A114324 << DiscreteMath`Combinatorica`; lst=Table[Length@Select[Partitions[n], (Times @@ # > n) &],{n,50}]
%t A114324 Table[Length[Select[IntegerPartitions[n],Times@@#>n&]],{n,0,20}] (* _Gus Wiseman_, Mar 27 2019 *)
%Y A114324 Cf. A001055, A028422, A096276, A114324, A301987, A319000, A319005, A319916, A325037, A325038, A325044.
%K A114324 nonn
%O A114324 0,7
%A A114324 _Giovanni Resta_, Feb 06 2006
%E A114324 a(0) = 1 prepended by _Gus Wiseman_, Mar 27 2019