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%I #6 May 03 2019 08:36:49
%S 1,1,1,2,2,3,3,4,5,5,6,8,7,9,11,10,12,15,13,16,19,18,20,24,22,26,29,
%T 28,31,37,33,38,43,42,44,52,48,55,59,58,62,72,65,74,80,80,82,94,88,99,
%U 103,104,108,123,114,126,133,135,137,155,145,161,166,169,174
%N Number of integer partitions of n whose k-th differences are strictly decreasing for all k >= 0.
%C 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 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 The Heinz numbers of these partitions are given by A325399.
%H Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts.</a>
%e The a(1) = 1 through a(9) = 5 partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e (21) (31) (32) (42) (43) (53) (54)
%e (41) (51) (52) (62) (63)
%e (61) (71) (72)
%e (431) (81)
%t Table[Length[Select[IntegerPartitions[n],And@@Table[Greater@@Differences[#,k],{k,0,Length[#]}]&]],{n,0,30}]
%Y Cf. A049988, A320466, A325353, A325354, A325358, A325391, A325396, A325399, A325404, A325406, A325457, A325468.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 02 2019
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