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 A325354 #6 May 03 2019 08:35:25
%S A325354 1,1,2,3,5,6,10,11,15,19,24,25,36,37,43,54,63,64,80,81,100,113,122,
%T A325354 123,151,166,178,195,217,218,269,270,295,316,332,372,424,425,447,472,
%U A325354 547,550,616,617,659,750,777,782,862,885,995,1032,1083,1090,1176,1275
%N A325354 Number of reversed integer partitions of n whose k-th differences are weakly increasing for all k.
%C A325354 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 A325354 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.
%C A325354 The Heinz numbers of these partitions are given by A325400.
%H A325354 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e A325354 The a(1) = 1 through a(8) = 15 reversed partitions:
%e A325354 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325354 (11) (12) (13) (14) (15) (16) (17)
%e A325354 (111) (22) (23) (24) (25) (26)
%e A325354 (112) (113) (33) (34) (35)
%e A325354 (1111) (1112) (114) (115) (44)
%e A325354 (11111) (123) (124) (116)
%e A325354 (222) (223) (125)
%e A325354 (1113) (1114) (224)
%e A325354 (11112) (11113) (1115)
%e A325354 (111111) (111112) (1124)
%e A325354 (1111111) (2222)
%e A325354 (11114)
%e A325354 (111113)
%e A325354 (1111112)
%e A325354 (11111111)
%t A325354 Table[Length[Select[Sort/@IntegerPartitions[n],And@@Table[OrderedQ[Differences[#,k]],{k,0,Length[#]}]&]],{n,0,30}]
%Y A325354 Cf. A007294, A240026, A325353, A325356, A325360, A325362, A325391, A325393, A325394, A325400, A325404, A325406, A325468.
%K A325354 nonn
%O A325354 0,3
%A A325354 _Gus Wiseman_, May 02 2019