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 A142156 #14 Feb 19 2018 03:34:50
%S A142156 1,1,-1,2,-1,-1,6,-2,-1,-3,24,-6,-2,-3,-13,120,-24,-6,-6,-13,-71,720,
%T A142156 -120,-24,-18,-26,-71,-461,5040,-720,-120,-72,-78,-142,-461,-3447,
%U A142156 40320,-5040,-720,-360,-312,-426,-922,-3447,-29093,362880,-40320,-5040,-2160,-1560
%N A142156 Triangle T(n,k)= n! if k=0, T(n,k) = -(n-k)!*A003319(k) if k > 0.
%F A142156 T(n,0) = A000142(n).
%F A142156 T(n,k) = -A141476(n-1,k-1), k > 0.
%F A142156 Sum_{k=0..n} |T(n,k)| = 2*n! = A098558(n).
%e A142156 Triangle begins
%e A142156 1;
%e A142156 1, -1;
%e A142156 2, -1, -1;
%e A142156 6, -2, -1, -3;
%e A142156 24, -6, -2, -3, -13;
%e A142156 120, -24, -6, -6, -13, -71;
%e A142156 720, -120, -24, -18, -26, -71, -461;
%t A142156 (* b = A003319 *) b[0]=0; b[n_] := b[n] = n! - Sum[k! b[n-k], {k, 1, n-1}]; T[n_, 0] := n!; T[n_, k_] := -(n - k)! b[k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 18 2018 *)
%K A142156 sign,tabl
%O A142156 0,4
%A A142156 _Paul Curtz_, Sep 16 2008