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 A325850 #7 Jun 02 2019 00:48:50
%S A325850 1,1,2,4,18,72,446,2804,21560,184364,1788514
%N A325850 Number of permutations of {1..n} whose differences of all degrees are nonzero.
%C A325850 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 A325850 The a(1) = 1 through a(4) = 18 permutations:
%e A325850 (1) (12) (132) (1243)
%e A325850 (21) (213) (1324)
%e A325850 (231) (1342)
%e A325850 (312) (1423)
%e A325850 (2134)
%e A325850 (2143)
%e A325850 (2314)
%e A325850 (2413)
%e A325850 (2431)
%e A325850 (3124)
%e A325850 (3142)
%e A325850 (3241)
%e A325850 (3412)
%e A325850 (3421)
%e A325850 (4132)
%e A325850 (4213)
%e A325850 (4231)
%e A325850 (4312)
%t A325850 Table[Length[Select[Permutations[Range[n]],!MemberQ[Union@@Table[Differences[#,i],{i,Length[#]}],0]&]],{n,0,5}]
%Y A325850 Dominated by A295370, the case for only differences of degree 2.
%Y A325850 Cf. A049988, A175342, A238423, A279945, A325545, A325851, A325852, A325874, A325875.
%K A325850 nonn,more
%O A325850 0,3
%A A325850 _Gus Wiseman_, May 31 2019