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 A177974 #20 Sep 26 2023 06:25:06
%S A177974 1,1,1,1,2,1,1,3,3,1,1,4,0,4,1,1,5,-40,-40,5,1,1,6,-330,-480,-330,6,1,
%T A177974 1,7,-2478,-3990,-3990,-2478,7,1,1,8,-20104,-33264,-36960,-33264,
%U A177974 -20104,8,1,1,9,-181368,-301896,-344736,-344736,-301896,-181368,9,1
%N A177974 Triangle T(n,k) = n!/(n - k)! + n!/k! - n! read by rows, 0 <= k <= n.
%H A177974 Seiichi Manyama, <a href="/A177974/b177974.txt">Rows n = 0..139, flattened</a>
%F A177974 T(n,k) = n!/(n - k)! + n!/k! - n.
%F A177974 T(n,k) = A155162(n,k) - n!. - _Seiichi Manyama_, Sep 26 2023
%e A177974 Triangle begins:
%e A177974 1;
%e A177974 1, 1;
%e A177974 1, 2, 1;
%e A177974 1, 3, 3, 1;
%e A177974 1, 4, 0, 4, 1;
%e A177974 1, 5, -40, -40, 5, 1;
%e A177974 1, 6, -330, -480, -330, 6, 1;
%e A177974 1, 7, -2478, -3990, -3990, -2478, 7, 1;
%e A177974 1, 8, -20104, -33264, -36960, -33264, -20104, 8, 1;
%e A177974 1, 9, -181368, -301896, -344736, -344736, -301896, -181368, 9, 1;
%e A177974 ...
%t A177974 Flatten[Table[Table[n!/(n - k)! + n!/k! - n!, {k, 0, n}], {n, 0, 10}]]
%Y A177974 Cf. A155162.
%K A177974 sign,tabl
%O A177974 0,5
%A A177974 _Roger L. Bagula_, May 16 2010