This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A353505 #5 May 20 2022 08:51:38
%S A353505 0,0,1,2,3,5,7,11,17,24,35,47,66,89,121,162,214,276,362,464,599,763,
%T A353505 971,1219,1537,1918,2393,2966,3668,4512,5549,6784,8287,10076,12238,
%U A353505 14807,17898,21556,25931,31094,37243,44486,53075,63158,75069,89025,105447,124636
%N A353505 Number of integer partitions of n whose product is greater than the product of their multiplicities.
%e A353505 The a(0) = 0 through a(7) = 11 partitions:
%e A353505 . . (2) (3) (4) (5) (6) (7)
%e A353505 (21) (22) (32) (33) (43)
%e A353505 (31) (41) (42) (52)
%e A353505 (221) (51) (61)
%e A353505 (311) (222) (322)
%e A353505 (321) (331)
%e A353505 (411) (421)
%e A353505 (511)
%e A353505 (2221)
%e A353505 (3211)
%e A353505 (4111)
%t A353505 Table[Length[Select[IntegerPartitions[n],Times@@#>Times@@Length/@Split[#]&]],{n,0,30}]
%Y A353505 RHS (product of multiplicities) is counted by A266477, ranked by A005361.
%Y A353505 LHS (product of parts) is counted by A339095, ranked by A003963.
%Y A353505 The version for less instead of greater is A353504.
%Y A353505 The version for equality is A353506, ranked by A353503.
%Y A353505 A124010 gives prime signature, sorted A118914.
%Y A353505 A181819 gives prime shadow, with an inverse A181821.
%Y A353505 A353398 counts partitions with the same products of multiplicities as of shadows, ranked by A353399.
%Y A353505 Cf. A002033, A008284, A008619, A085629, A097318, A098859, A114640, A116608, A130091, A304678, A353394, A353507.
%K A353505 nonn
%O A353505 0,4
%A A353505 _Gus Wiseman_, May 19 2022