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 A325875 #5 Jun 02 2019 23:40:14
%S A325875 1,1,2,3,7,13,20,38,69,129,222,407,726,1313,2318,4146,7432,13296,
%T A325875 23759,42458,75714
%N A325875 Number of compositions of n whose differences of all degrees > 1 are nonzero.
%C A325875 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. If m is the length of the sequence, its differences of all degrees are the union of the zeroth through m-th differences.
%C A325875 A composition of n is a finite sequence of positive integers with sum n.
%C A325875 The case for all degrees including 1 is A325851.
%H A325875 Gus Wiseman, <a href="/A325325/a325325.txt">Sequences counting and ranking integer partitions by the differences of their successive parts</a>
%e A325875 The a(1) = 1 through a(6) = 20 compositions:
%e A325875 (1) (2) (3) (4) (5) (6)
%e A325875 (11) (12) (13) (14) (15)
%e A325875 (21) (22) (23) (24)
%e A325875 (31) (32) (33)
%e A325875 (112) (41) (42)
%e A325875 (121) (113) (51)
%e A325875 (211) (122) (114)
%e A325875 (131) (132)
%e A325875 (212) (141)
%e A325875 (221) (213)
%e A325875 (311) (231)
%e A325875 (1121) (312)
%e A325875 (1211) (411)
%e A325875 (1122)
%e A325875 (1131)
%e A325875 (1212)
%e A325875 (1311)
%e A325875 (2121)
%e A325875 (2211)
%e A325875 (11211)
%t A325875 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MemberQ[Union@@Table[Differences[#,i],{i,2,Length[#]}],0]&]],{n,0,10}]
%Y A325875 Cf. A049988, A238423, A325325, A325468, A325545, A325849, A325850, A325851, A325852, A325874, A325876.
%K A325875 nonn,more
%O A325875 0,3
%A A325875 _Gus Wiseman_, Jun 02 2019