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%I #9 Jan 03 2021 14:00:37
%S 1,1,1,2,2,3,3,5,6,6,9,11,11,15,19,19,26,31,31,41,49,53,62,75,81,97,
%T 112,124,145,171,175,215,244,274,307,344,388,446,497,561,599,700,779,
%U 881,981,1054,1184,1340,1500,1669,1767,2031,2237,2486,2765,2946,3300
%N Number of (strict) integer partitions of n whose differences of all degrees are nonzero.
%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). The zeroth differences are the sequence itself, while k-th differences for k > 0 are the differences of the (k-1)-th differences. The differences of all degrees of a sequence are the union of its zeroth through m-th differences, where m is the length of the sequence.
%H Fausto A. C. Cariboni, <a href="/A325852/b325852.txt">Table of n, a(n) for n = 0..250</a>
%e The a(1) = 1 through a(11) = 11 partitions (A = 10, B = 11):
%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
%e (21) (31) (32) (42) (43) (53) (54) (64) (65)
%e (41) (51) (52) (62) (63) (73) (74)
%e (61) (71) (72) (82) (83)
%e (421) (431) (81) (91) (92)
%e (521) (621) (532) (A1)
%e (541) (542)
%e (631) (632)
%e (721) (641)
%e (731)
%e (821)
%t Table[Length[Select[IntegerPartitions[n],!MemberQ[Union@@Table[Differences[#,i],{i,Length[#]}],0]&]],{n,0,30}]
%Y The case for only degrees > 1 is A325874.
%Y Cf. A049988, A175342, A238423, A279945, A295370, A325328, A325468, A325545, A325850, A325851, A325875.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 31 2019
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