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 A325851 #4 Jun 02 2019 00:48:58
%S A325851 1,1,1,3,4,7,12,21,35,58,102,171,284,485,819,1355,2301,3884,6528,
%T A325851 10983,18380,30824,51851
%N A325851 Number of (strict) compositions of n whose differences of all degrees are nonzero.
%C A325851 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.
%e A325851 The a(1) = 1 through a(7) = 21 compositions:
%e A325851 (1) (2) (3) (4) (5) (6) (7)
%e A325851 (12) (13) (14) (15) (16)
%e A325851 (21) (31) (23) (24) (25)
%e A325851 (121) (32) (42) (34)
%e A325851 (41) (51) (43)
%e A325851 (131) (132) (52)
%e A325851 (212) (141) (61)
%e A325851 (213) (124)
%e A325851 (231) (142)
%e A325851 (312) (151)
%e A325851 (1212) (214)
%e A325851 (2121) (232)
%e A325851 (241)
%e A325851 (313)
%e A325851 (412)
%e A325851 (421)
%e A325851 (1213)
%e A325851 (1312)
%e A325851 (2131)
%e A325851 (3121)
%e A325851 (12121)
%t A325851 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],!MemberQ[Union@@Table[Differences[#,i],{i,Length[#]}],0]&]],{n,0,10}]
%Y A325851 The case for only degrees > 1 is A325875.
%Y A325851 Cf. A049988, A175342, A238423, A295370, A325328, A325545, A325850, A325852, A325874.
%K A325851 nonn,more
%O A325851 0,4
%A A325851 _Gus Wiseman_, May 31 2019