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 A319876 #39 Dec 13 2018 09:17:54
%S A319876 1,0,2,0,2,3,1,0,0,14,0,9,0,1,0,0,24,50,20,0,15,10,0,0,1,0,0,0,264,0,
%T A319876 340,0,40,0,60,0,15,0,0,0,1,0,0,0,720,1764,504,0,1120,630,0,0,70,105,
%U A319876 105,0,0,21,0,0,0,0,1,0,0,0,0,13488,0,14112,0,3724,0
%N A319876 Irregular triangle read by rows where T(n,k) is the number of permutations of {1,...,n} whose action on 2-element subsets of {1,...,n} has k cycles.
%C A319876 The permutation
%C A319876 1 -> 1
%C A319876 2 -> 2
%C A319876 3 -> 4
%C A319876 4 -> 3
%C A319876 acts on unordered pairs of distinct elements of {1,2,3,4} to give
%C A319876 (1,2) -> (1,2)
%C A319876 (1,3) -> (1,4)
%C A319876 (1,4) -> (1,3)
%C A319876 (2,3) -> (2,4)
%C A319876 (2,4) -> (2,3)
%C A319876 (3,4) -> (3,4)
%C A319876 which has 4 cycles
%C A319876 (1,2)
%C A319876 (1,3) <-> (1,4)
%C A319876 (2,3) <-> (2,4)
%C A319876 (3,4)
%C A319876 so is counted under T(4,4).
%F A319876 A000088(n) = (1/n!) * Sum_k 2^k * T(n,k).
%e A319876 Triangle begins:
%e A319876 1
%e A319876 0 2
%e A319876 0 2 3 1
%e A319876 0 0 14 0 9 0 1
%e A319876 0 0 24 50 20 0 15 10 0 0 1
%e A319876 0 0 0 264 0 340 0 40 0 60 0 15 0 0 0 1
%e A319876 The T(4,4) = 9 permutations: (1243), (1324), (1432), (2134), (2143), (3214), (3412), (4231), (4321).
%t A319876 Table[Length[Select[Permutations[Range[n]],PermutationCycles[Ordering[Map[Sort,Subsets[Range[n],{2}]/.Rule@@@Table[{i,#[[i]]},{i,n}],{1}]],Length]==k&]],{n,5},{k,0,n*(n-1)/2}]
%Y A319876 Row n has A000124(n - 1) terms. Row sums are the factorial numbers A000142.
%Y A319876 Cf. A000088, A000612, A000665, A000666, A003180, A050535, A070166, A317794, A317795.
%K A319876 nonn,tabf
%O A319876 1,3
%A A319876 _Gus Wiseman_, Dec 12 2018