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 A363946 #6 Jun 30 2023 23:54:36
%S A363946 1,0,1,0,1,1,0,1,1,1,0,1,3,0,1,0,1,3,2,0,1,0,1,6,3,0,0,1,0,1,6,4,3,0,
%T A363946 0,1,0,1,11,5,4,0,0,0,1,0,1,11,13,0,4,0,0,0,1,0,1,18,9,8,5,0,0,0,0,1,
%U A363946 0,1,18,21,10,0,5,0,0,0,0,1
%N A363946 Triangle read by rows where T(n,k) is the number of integer partitions of n with high mean k.
%C A363946 Extending the terminology of A124944, the "high mean" of a multiset is obtained by taking the mean and rounding up.
%e A363946 Triangle begins:
%e A363946 1
%e A363946 0 1
%e A363946 0 1 1
%e A363946 0 1 1 1
%e A363946 0 1 3 0 1
%e A363946 0 1 3 2 0 1
%e A363946 0 1 6 3 0 0 1
%e A363946 0 1 6 4 3 0 0 1
%e A363946 0 1 11 5 4 0 0 0 1
%e A363946 0 1 11 13 0 4 0 0 0 1
%e A363946 0 1 18 9 8 5 0 0 0 0 1
%e A363946 0 1 18 21 10 0 5 0 0 0 0 1
%e A363946 0 1 29 28 12 0 6 0 0 0 0 0 1
%e A363946 0 1 29 32 18 14 0 6 0 0 0 0 0 1
%e A363946 0 1 44 43 23 16 0 7 0 0 0 0 0 0 1
%e A363946 0 1 44 77 27 19 0 0 7 0 0 0 0 0 0 1
%e A363946 Row n = 7 counts the following partitions:
%e A363946 . (1111111) (4111) (511) (61) . . (7)
%e A363946 (3211) (421) (52)
%e A363946 (31111) (331) (43)
%e A363946 (2221) (322)
%e A363946 (22111)
%e A363946 (211111)
%t A363946 meanup[y_]:=If[Length[y]==0,0,Ceiling[Mean[y]]];
%t A363946 Table[Length[Select[IntegerPartitions[n],meanup[#]==k&]],{n,0,15},{k,0,n}]
%Y A363946 Row sums are A000041.
%Y A363946 Column k = 2 is A026905 redoubled, ranks A363950.
%Y A363946 For median instead of mean we have triangle A124944, low A124943.
%Y A363946 For mode instead of mean we have rank stat A363486, high A363487.
%Y A363946 For median instead of mean we have rank statistic A363942, low A363941.
%Y A363946 The rank statistic for this triangle is A363944.
%Y A363946 The version for low mean is A363945, rank statistic A363943.
%Y A363946 For mode instead of mean we have triangle A363953, low A363952.
%Y A363946 A008284 counts partitions by length, A058398 by mean.
%Y A363946 A051293 counts subsets with integer mean, median A000975.
%Y A363946 A067538 counts partitions with integer mean, strict A102627, ranks A316413.
%Y A363946 A349156 counts partitions with non-integer mean, ranks A348551.
%Y A363946 Cf. A002865, A025065, A237984, A327472, A327482, A344296, A362612, A363723, A363724, A363731, A363948.
%K A363946 nonn,tabl
%O A363946 0,13
%A A363946 _Gus Wiseman_, Jun 30 2023