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 A325466 #7 May 04 2019 08:32:06
%S A325466 1,1,0,1,1,0,1,2,0,0,1,3,1,0,0,1,3,2,1,0,0,1,5,4,0,1,0,0,1,4,6,3,0,1,
%T A325466 0,0,1,6,6,4,3,1,1,0,0,1,6,10,4,2,4,1,2,0,0,1,7,12,8,3,3,4,1,2,1,0,1,
%U A325466 6,13,11,2,11,3,4,0,3,1,1,1,10,16,7,10,10
%N A325466 Triangle read by rows where T(n,k) is the number of reversed integer partitions of n with k distinct differences of any degree > 0.
%C A325466 The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2).
%C A325466 The zeroth differences of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences.
%e A325466 Triangle begins:
%e A325466 1
%e A325466 1 0
%e A325466 1 1 0
%e A325466 1 2 0 0
%e A325466 1 3 1 0 0
%e A325466 1 3 2 1 0 0
%e A325466 1 5 4 0 1 0 0
%e A325466 1 4 6 3 0 1 0 0
%e A325466 1 6 6 4 3 1 1 0 0
%e A325466 1 6 10 4 2 4 1 2 0 0
%e A325466 1 7 12 8 3 3 4 1 2 1 0
%e A325466 1 6 13 11 2 11 3 4 0 3 1 1
%e A325466 1 10 16 7 10 10 6 6 5 1 1 2 1
%e A325466 1 7 18 14 7 16 11 6 4 8 0 5 0 1
%e A325466 1 9 20 18 10 20 13 10 10 4 5 5 2 2 2
%e A325466 1 10 26 18 10 24 13 19 13 10 6 6 2 8 1 2
%e A325466 1 11 25 24 16 28 19 24 14 15 9 10 9 5 2 7 1
%e A325466 Row 7 counts the following reversed partitions (empty columns not shown):
%e A325466 (7) (16) (115) (133) (11122)
%e A325466 (25) (124) (1123)
%e A325466 (34) (223) (1222)
%e A325466 (1111111) (1114)
%e A325466 (11113)
%e A325466 (111112)
%e A325466 Row 9 counts the following reversed partitions (empty columns not shown):
%e A325466 (9) (18) (117) (126) (1125) (1134) (11223) (111222)
%e A325466 (27) (135) (144) (11124) (1224) (1111122)
%e A325466 (36) (225) (1233) (11133)
%e A325466 (45) (234) (12222) (111123)
%e A325466 (333) (1116)
%e A325466 (111111111) (2223)
%e A325466 (11115)
%e A325466 (111114)
%e A325466 (1111113)
%e A325466 (11111112)
%t A325466 Table[Length[Select[Reverse/@IntegerPartitions[n],Length[Union@@Table[Differences[#,i],{i,1,Length[#]}]]==k&]],{n,0,16},{k,0,n}]
%Y A325466 Row sums are A000041. Column k = 1 is A088922.
%Y A325466 Cf. A098859, A279945, A325242, A325324, A325325, A325349, A325404, A325405, A325406, A325468.
%K A325466 nonn,tabl
%O A325466 0,8
%A A325466 _Gus Wiseman_, May 04 2019