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 A352832 #7 May 15 2022 11:48:56
%S A352832 0,1,1,1,4,3,7,7,14,19,24,32,46,60,85,109,140,179,239,300,397,495,636,
%T A352832 790,995,1239,1547,1926,2396,2942,3643,4432,5435,6602,8038,9752,11842,
%U A352832 14292,17261,20714,24884,29733,35576,42375,50522,60061,71363,84551,100101
%N A352832 Number of reversed integer partitions y of n with exactly one fixed point y(i) = i.
%C A352832 A reversed integer partition of n is a finite weakly increasing sequence of positive integers summing to n.
%e A352832 The a(0) = 0 through a(8) = 14 partitions (empty column indicated by dot):
%e A352832 . (1) (11) (111) (13) (14) (15) (16) (17)
%e A352832 (22) (1112) (114) (115) (116)
%e A352832 (112) (11111) (222) (1123) (134)
%e A352832 (1111) (1113) (11113) (224)
%e A352832 (1122) (11122) (233)
%e A352832 (11112) (111112) (1115)
%e A352832 (111111) (1111111) (2222)
%e A352832 (11114)
%e A352832 (11123)
%e A352832 (11222)
%e A352832 (111113)
%e A352832 (111122)
%e A352832 (1111112)
%e A352832 (11111111)
%e A352832 For example, the reversed partition (2,2,4) has a unique fixed point at the second position.
%t A352832 pq[y_]:=Length[Select[Range[Length[y]],#==y[[#]]&]];
%t A352832 Table[Length[Select[Reverse/@IntegerPartitions[n],pq[#]==1&]],{n,0,30}]
%Y A352832 * = unproved
%Y A352832 *The non-reverse version is A001522, ranked by A352827, strict A352829.
%Y A352832 *The non-reverse complement is A064428, ranked by A352826, strict A352828.
%Y A352832 This is column k = 1 of A238352.
%Y A352832 For no fixed point: counted by A238394, ranked by A352830, strict A025147.
%Y A352832 For > 0 fixed points: counted by A238395, ranked by A352872, strict A096765.
%Y A352832 The version for compositions is A240736, complement A352520.
%Y A352832 These partitions are ranked by A352831.
%Y A352832 A000700 counts self-conjugate partitions, ranked by A088902.
%Y A352832 A008290 counts permutations by fixed points, nonfixed A098825.
%Y A352832 A115720 and A115994 count partitions by their Durfee square.
%Y A352832 A238349 counts compositions by fixed points, complement A352523.
%Y A352832 A352822 counts fixed points of prime indices.
%Y A352832 A352833 counts partitions by fixed points.
%Y A352832 Cf. A064410, A177510, A257990, A325187, A351983, A352824, A352825.
%K A352832 nonn
%O A352832 0,5
%A A352832 _Gus Wiseman_, Apr 08 2022